1.DBH Azalera eta perimetroa zirkuluarena Kalkulatu zirkulu baten perimetroa eta zalera bere erradioa #r m izanik

Perimetroa={#1} m

Azalera={#2} m²

]]> 1.0000000 0.0000000 0 editor 15 0 Irudi geometrikoen aldeak Bete hutsuneak:

Bost alde dituen irudi geometrikoari {#1} deitzen zaio, eta sei alde dituen irudiari {#2} .

Erantzun egokia aukeratu:

r zirkunferentzia baten erradioa izanik, {#3} kalkulatzeko «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«mo»§#183;«/mo»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math» erabiltzen dugu; eta {#4} kalkutzeko «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»§#183;«/mo»«mi»§#960;«/mi»«mo»§#183;«/mo»«mi»r«/mi»«/math»

]]> 4.0000000 0.3333333 0 <question/> Kalkulatu laukizuzen baten perimetroa, diagonala eta azalera Laukizuzen baten oinarria eta azalera emanda #a cm i #b cm, kalkulatu:

#graph

Perimetroaren balioa {#1} cm

Diagonala {#2} cm

Azalera {#3} cm²

]]> 3.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>/</mo><mn>2</mn><mo>,</mo><mi>b</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graph</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>poligono</mi><mfenced><mrow><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>b</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>2</mn><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Trapezio zuzen baten perimetroa eta azalera

Kalkulatu trapezio zuzen baten perimetroa eta azalera jakinik oinarri handiaren luzera #B cm ,oinarri txikiarena #b cm, altueraren luzera #h cm eta alde zeiharrarena #a cm direla.

Perimetroaren balioa {#1} cm

Azaleraren balioa {#2} cm²

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Terna</mi><mo> </mo><mi>pitagòrica</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>m</mi><mo>·</mo><mi>n</mi><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>,</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>m</mi><mo>·</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mrow><mi>B</mi><mo>+</mo><mi>b</mi></mrow><mn>2</mn></mfrac><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>B</mi><mo>+</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>perdoi_o_tolerantzia</mi><mo> </mo><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>4.6154</mn><mo>,</mo><mn>13</mn><mo>,</mo><mi>B</mi><mo>,</mo><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Unitate aldaketak era konplexuan idatzi Era konplexuan idatzi:

#a km²= {#1}km² {#2}hm² {#3}dam² {#4}m² {#5}dm²

]]> 5.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>{</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi><mo>}</mo><mo>=</mo><mo>{</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo> </mo><mi>zerekin</mi><mo> </mo><mi>i</mi><mo> </mo><mi>an</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><msup><csymbol definitionURL="http://.../units/meter#k">km</csymbol><mn>2</mn></msup><mo> </mo><mi>a2</mi><msup><csymbol definitionURL="http://.../units/meter#h">hm</csymbol><mn>2</mn></msup><mo> </mo><mi>a3</mi><msup><csymbol definitionURL="http://.../units/meter#da">dam</csymbol><mn>2</mn></msup><mo> </mo><mi>a4</mi><msup><csymbol definitionURL="http://.../units/meter">m</csymbol><mn>2</mn></msup><mo> </mo><mi>a5</mi><msup><csymbol definitionURL="http://.../units/meter#d">dm</csymbol><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>bihurtu</mi><mo>(</mo><mi>a</mi><mo>,</mo><msup><csymbol definitionURL="http://.../units/meter#k">km</csymbol><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>koefiziente</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.1203</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Unitate aldaketak m^2 Unitate aldaketak m²:

#a km² ={#1} m².
#b cm² ={#2} m².
#c area(a) ={#3} m².
#d hektarea(ha) ={#4} m².

]]> 4.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>10000</mn><mo>,</mo><mn>30000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>koefiziente</mi><mo>(</mo><mi>bihurtu</mi><mo>(</mo><mi>aa</mi><mo> </mo><msup><csymbol definitionURL="http://.../units/meter">m</csymbol><mn>2</mn></msup><mo>,</mo><msup><csymbol definitionURL="http://.../units/meter#k">km</csymbol><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>koefiziente</mi><mo>(</mo><mi>bihurtu</mi><mo>(</mo><mi>bb</mi><mo> </mo><msup><csymbol definitionURL="http://.../units/meter">m</csymbol><mn>2</mn></msup><mo>,</mo><msup><csymbol definitionURL="http://.../units/meter#c">cm</csymbol><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>koefiziente</mi><mo>(</mo><mi>bihurtu</mi><mo>(</mo><mi>cc</mi><mo> </mo><msup><csymbol definitionURL="http://.../units/meter">m</csymbol><mn>2</mn></msup><mo>,</mo><msup><csymbol definitionURL="http://.../units/meter#da">dam</csymbol><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>koefiziente</mi><mo>(</mo><mi>bihurtu</mi><mo>(</mo><mi>dd</mi><mo> </mo><msup><csymbol definitionURL="http://.../units/meter">m</csymbol><mn>2</mn></msup><mo>,</mo><msup><csymbol definitionURL="http://.../units/meter#h">hm</csymbol><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>,</mo><mn>2.9</mn><mo>*</mo><msup><mn>10</mn><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 2.DBH Azalerak eta bolumenak_Cloze Irudian hiru zuzen ikusten dira (gorria, urdina eta berdea). Hiruren artean eremu bat mugatzen dute abzisen ardatzaren kontra. Kalkulatu behar duzu eremu horren azalera ta segidan idatzi.

#Graf3

{#1}

Eremu hori balitz #h altuera duen prisma baten oinarria....zenbat balioko zuen prisma horren bolumena? Aukeratu zerrendan:

{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>c</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>C</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mi>D</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Graf1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Graf2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verde</mi><mo>,</mo><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Graf3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>q</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>azul</mi><mo>,</mo><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Al</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>At</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>b</mi><mo>-</mo><mi>c</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>d</mi><mo>-</mo><mi>a</mi></mrow></mfenced></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ao</mi><mo>=</mo><mi>Al</mi><mo>+</mo><mi>At</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Bol</mi><mo>=</mo><mi>Ao</mi><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><msup><mi>d</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><msup><mi>b</mi><mn>3</mn></msup><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Geometria_Cloze Kalkulatu eta idatzi eremuan karratuaren azalera:

#graf

{#1}

Karratu hau #h cm altuera duen prisma baten oinarria balitz, zenbat cm³-ko bolumena izango zuen prisma horrek? Kalkulatu eta aukeratu erantzun zuzena:

{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mi>estado_geometría</mi><mfenced><mtext>"2D"</mtext></mfenced><mtext xml:lang="es">variables</mtext></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>∈</mo><integers/></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>∈</mo><integers/></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>∈</mo><integers/></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mtd></mtr></mtable><mrow><mi>área</mi><mo>(</mo><mi>polígono_regular</mi><mo>(</mo><mn>4</mn><mo>,</mo><mi>A</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>polígono_regular</mi><mo>(</mo><mn>4</mn><mo>,</mo><mi>A</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dib</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>dib</mi><mo>,</mo><mi>L</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verde</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>área</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>área</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mo>(</mo><mi>R</mi><mo>*</mo><mi>h</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mi>R</mi><mo>*</mo><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>*</mo><mi>h</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> GEOMETRIA_ZIRKUNF. Kalkulatu irudiaren zirkunferentziaren perimetro eta idatzi eremuan. Gero, kalkulatu bere azalera eta aukeratu eskeintzen diren datuen artean:

#graf_Z

{#1}

{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mfenced><mrow><mi>p1</mi><mo>-</mo><mi>c1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>p2</mi><mo>-</mo><mi>c2</mi></mrow></mfenced><mn>2</mn></msup></mrow></msqrt></mtd></mtr><mtr><mtd><mi>L</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>π</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>t</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>Z</mi><mo>=</mo><mi>cfr</mi><mfenced><mrow><mi>C</mi><mo>,</mo><mi>r</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mi>área</mi><mo>(</mo><mi>Z</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf_Z</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>Z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>π</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>azf1</mi><mo>=</mo><mfenced><mrow><mn>2</mn><mo>*</mo><mi>π</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>azf2</mi><mo>=</mo><mfenced><mrow><mi>π</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>azf3</mi><mo>=</mo><mi>π</mi><mo>*</mo><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Lehen mailako ekuazioa Lehen mailako ekuazio honen ebazpena

#a·x-#b·x+#c=#d·x+#e

]]> 1.0000000 0.1000000 0 0 #sol Oso ondo!!!!!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>12</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>-</mo><mi>d</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>X</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>e</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>n</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>N</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>d</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>e</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>M</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Prisma 1 Hona hemen prisma baten garapena:

Zenbat aurpegi ditu prismak? {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»m«/mi»«mspace linebreak=¨newline¨/»«mi»b«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»m«/mi»«mspace linebreak=¨newline¨/»«mi»c«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»m«/mi»«/math»

Kalkulatu prismaren azalera osoa aurpegu bakoitzarena kalkulatuz: (197 orrialdea)

A_osoa = {#2} cm²

Kalkulatu prismaren bolumena

B = {#3} cm³

]]> 1.0000000 0.0000000 0 editor 15 1 <question/> Triangelu Baten Hipotenusa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨»K«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»h«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»h«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»p«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»j«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«/math»

#graf

Eman emaitza unitateetara hurbilduta beharrik balego

h = {#1} metro

Zein da Triangeluaren perimetroa?

{#2} metro

Kalkulatu Triangeluaren azalera:

{#3} m²

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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Triangelu eskaleno baten altuera eta azalera «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨»K«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi 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mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»j«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»h«/mi»«mo 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mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»z«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»d«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»r«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»a«/mi»«/math»

#graf

Eman emaitza era honetan 34.5 adibidez, hamartar batekin nahiko (hurbilketa eginez).

altuera = {#1} metro

Zein da oinarriaren luzera?

oina = {#2}

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mo>{</mo><mi>sa</mi><mo>,</mo><mi>alde2</mi><mo>,</mo><mi>alde3</mi><mo>,</mo><mi>alde1</mi><mo>,</mo><mi>alde4</mi><mo>,</mo><mi>alde5</mi><mo>}</mo><mo>,</mo><mo>{</mo><mo>{</mo><mo>}</mo><mo>,</mo><mo>{</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>berdea</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>beltz</mi><mo>}</mo><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>96</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>96</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>+</mo><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>69.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>118.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>oina</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1365.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zatikien arteko eragiketak. Eragin kalkuladorea erabili barik:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mfrac»«mn»7«/mn»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mn»4«/mn»«mn»5«/mn»«/mfrac»«/mrow»«/mfenced»«mo»·«/mo»«mfenced»«mrow»«mfrac»«mn»8«/mn»«mn»7«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«mo»·«/mo»«mfrac»«mn»5«/mn»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«mo»-«/mo»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«mo»=«/mo»«/math»

]]> 1.0000000 0.1000000 0 true true abc #p

]]> Super bien.

]]> #np1

]]> #np2

]]> #np3

perimetroa={#1}·«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«/math»m

azalera={#2}m²

]]> 1.MAILAKO EKUAZIOAREN EBAZPENA EGIN

]]> 1.0000000 0.0000000 0 editor 15 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mo>+</mo><mn>100</mn><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>p</mi><mo>:=</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>gradu</mi><mo> </mo><mo>(</mo><mi>p</mi><mo>)</mo><mo><</mo><mn>2</mn><mo>∧</mo><mi>gradu</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>></mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">add</data><data name="casSession"><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></data></localData></question> Aldagai estatistikoak Hurrengo maitazun taula emanda, kalkula ezazu batez besteko aritmetikoa:

x_i	_ni
#x1	#n1
#x2	#n2
#x3	#n3
#x4	#n4
#x5	#n5

]]> 1.0000000 0.0000000 0 editor 15 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerancia</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>k</mi><mo>.</mo><mo>.</mo><mi>l</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mi>x2</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>r</mi><mo>(</mo><mi>x3</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>r</mi><mo>(</mo><mi>x4</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>r</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mi>lista_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo><</mo><mi>n2</mi></mrow><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>x2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo><</mo><mi>n3</mi></mrow><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>x3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo><</mo><mi>n4</mi></mrow><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>x4</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo><</mo><mi>n5</mi></mrow><mtable><mtr><mtd><mi>X</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>x5</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>media</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">false</data><data name="casSession"/></localData></question> Aljebra LABURTU Laburtu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b«/mi»«mo»·«/mo»«mi»y«/mi»«mo»-«/mo»«mi»#c«/mi»«mo»·«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#d«/mi»«mo»·«/mo»«mi»y«/mi»«/math»

]]> Ondo !!

]]> 1.0000000 0.1000000 0 0 #erantzuna Aurrera!

]]> <question><wirisCasSession><session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>erantzuna</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command></group></library></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #erantzuna </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Aljebra1
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b«/mi»«mo»·«/mo»«mi»y«/mi»«mo»-«/mo»«mi»#c«/mi»«mo»·«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#d«/mi»«mo»·«/mo»«mi»y«/mi»«/math»
]]> 1.0000000 0.1000000 0 0 #erantzuna <question><wirisCasSession><session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>erantzuna</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command></group></library></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #erantzuna </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Aljebra5
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b«/mi»«mo»·«/mo»«mi»y«/mi»«mo»-«/mo»«mo»(«/mo»«mi»#c«/mi»«mo»·«/mo»«mi»x«/mi»«mo»-«/mo»«mi»#d«/mi»«mo»·«/mo»«mi»y«/mi»«mo»)«/mo»«/math»
]]> 1.0000000 0.1000000 0 true true abc #erantzuna Ederto #bestea Kontuz <question><wirisCasSession><session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>erantzuna</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bestea</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>y</mi></math></input></command></group></library></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Bi puntutatik pasatzen den zuzena «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mi»s«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mi»k«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»s«/mi»«mi»a«/mi»«mi»l«/mi»«mi»d«/mi»«mi»i«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»g«/mi»«mi»i«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»e«/mi»«mi»z«/mi»«mi»u«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»A«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»u«/mi»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»k«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»s«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»u«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»k«/mi»«mi»u«/mi»«mi»a«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mi»k«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»a«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 1.0000000 0 Verdadero Oso ondo

]]> Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>≠</mo><mi>c</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>b</mi><mo>≠</mo><mi>d</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>·</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow></mfrac><mo>·</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>·</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>·</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ek</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>sol</mi><mo>,</mo><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:</mo><mo>=</mo><mfenced><mrow><mi>sol</mi><mo>=</mo><mi>ek</mi></mrow></mfenced><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>,</mo><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>7</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>50</mn><mn>7</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>62</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>7</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>34</mn><mn>7</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>7</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>34</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ek</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>7</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>50</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Biderkadurak Nabarmenak1 Kalkulatu ondoko biderkadura nabarmena hau: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»

{#1}

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak_1</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mo>·</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Bierkadurak Nabarmenak 2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»u«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mi»g«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»i«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»k«/mi»«mi»a«/mi»«mi»d«/mi»«mi»u«/mi»«mi»r«/mi»«mi»a«/mi»«mi»k«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«/math»

{#1}

f(x) = #f

]]> 1.0000000 0.1000000 0 true true none «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mo»±«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»-«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mo»§#8734;«/mo»«mo»,«/mo»«mn»1«/mn»«mo»]«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mo»§#8734;«/mo»«mo»,«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

#graf

a) Adierazi definizio eremua eta ibiltartea.

b) Aztertu jarraitasuna.

c) Kalkulatu ardatzekiko ebaki-puntuak.

d) Aztertu gorakortasuna eta beherakortasuna.

e) Kalkulatu maximo eta minimo erlatiboak.

]]> 1.0000000 0.0000000 0 editor 15 1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>:</mo><mo>=</mo><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>f</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>:</mo><mo>=</mo><mo>-</mo><mfenced close="|" open="|"><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>g</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>:</mo><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mi>h</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>:</mo><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T4</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mi>i</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>:</mo><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T5</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>15</mn><mo>,</mo><mn>15</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T5</mi><mo>,</mo><mi>j</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>d4</mi><mo>,</mo><mi>d5</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">false</data><data name="casSession"/></localData></question> Funtzio baten grafikoa Grafika bat dator funtzioarekin «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#h«/mi»«/math»?
#p

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #g1

]]> f(x)=#f1 #g2

]]> f(x)=#f2 #g3

]]> f(x)=#f3 #g4

]]> f(x)=#f4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mtext>({zentroa=puntu(0,0),zabalera=</mtext><mn>20</mn><mtext>,altuera=</mtext><mn>20</mn><mtext>})</mtext><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mtext>({zentroa=puntu(0,0),zabalera=</mtext><mn>20</mn><mtext>,altuera=</mtext><mn>20</mn><mtext>})</mtext><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mtext>{zentroa=puntu(0,0),zabalera=</mtext><mn>20</mn><mtext>,altuera=</mtext><mn>20</mn><mtext>}</mtext><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mtext>{zentroa=puntu(0,0),zabalera=</mtext><mn>20</mn><mtext>,altuera=</mtext><mn>20</mn><mtext>}</mtext><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s4</mi><mo>,</mo><mi>f4</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Gorputz geometrikoak Ikosaedroak {1:MULTICHOICE:%100%20#Oso ondo~%0%6#Hexaedroak ditu 6 aurpegi~%0%12#Dodekaedroak ditu 12 aurpegi} aurpegi ditu.

Oktaedroak {1:MULTICHOICE:%100%8#Oso ondo~%0%4#Tetraedroak ditu 4 aurpegi~%0%12#Dodekaedroak ditu 12 aurpegi} aurpegi ditu.

Kalkulatu 12 cm-ko altuera duen piramide erregular baten guztizko azalera, bere oinarria 10 cm-ko aldea duen karratu bat dela jakinik.

Erantzuna: {2:SHORTANSWER:%100%360#Oso ondo} cm²

]]> Gogoratu poliedroak aurpegi kopuruaren arabera izendatzen direla.

]]> 0.1000000 0

]]>

]]> Grafikoa eta Funtzioa bat datoz? Adierazi jarraian azaltzen den grafikoa funtzio honi dagokion f(x) = #fx

#graf

]]> 1.0000000 1.0000000 0 Verdadero Oso ondo!

]]> Falso Kontuz, fijatu zaitez ea gorakorra edo beherakorra den

]]> 1.0000000 0.3333333 0 0 #erantzuna]]> Oso ondo!!

Soluziorik ez badauka era honetan idatziko duzugiltzak erabiliz

Emaitza, adibidez, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mn»5«/mn»«mn»3«/mn»«/mfrac»«/math» , era honetan idazten duzu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨{¨»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»5«/mn»«mn»3«/mn»«/mfrac»«/mrow»«/mfenced»«/mfenced»«/math»
Emaitz bat baino gehiago izatekotan: era honetan idazten duzu:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨{¨»«mrow»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«mo»,«/mo»«mfenced close=¨}¨ open=¨{¨»«mrow»«mi»x«/mi»«mo»=«/mo»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math»

]]> OSO ONDO!

]]> 1.0000000 0.5000000 0 0 #s Aurrera!

]]> Eragiketak egiterakoan gogoratu eragiketen hierarkia!

]]> 1.0000000 0.2500000 0 0 #zenba]]> Zorionak!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>1</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>funtzio</mi><mo> </mo><mo>(</mo><mi>P</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>s</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zenba</mi><mo>=</mo><mi>Q</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>↦</mo><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>X</mi><mn>5</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>X</mi><mn>4</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><msup><mi>X</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>X</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>X</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zenba</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>92</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>z</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">b</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Martamatika Funtzioak Emparejamiento Lotu hurrengo grafikoak dagozkien adierazpen aljebraikoekin:

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #g1

]]> f(x)=#f1 #g2

]]> f(x)=#f2 #g3

]]> f(x)=#f3 #g4

]]> f(x)=#f4 f(x)=#f5 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><mi>adierazi</mi><mo> </mo><mo>(</mo><mi>s4</mi><mo>,</mo><mi>f4</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Martamatika Funtzioak Opción multiple f(x) =#f funtzioa emanda, hurrengo puntuetatik, zein da funtzioaren irudikapen grafikokoa?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #puntu1

]]> Oso ondo!

]]> #puntu2

]]> Eragiketak birpasatu!

]]> #puntu3

]]> Eragiketak birpasatu!

]]> #puntu4

]]> Eragiketak birpasatu!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>funtzio</mi><mo> </mo><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bal</mi><mo>=</mo><mo> </mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu1</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>bal</mi><mo>,</mo><mo> </mo><mi>g</mi><mo>(</mo><mi>bal</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu2</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu3</mi><mo>=</mo><mi>puntu</mi><mo> </mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu4</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>↦</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>23</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>puntu4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Martamatika Funtzioak Verdadero Falso Grafiko honek funtzio bat adierazten du?

#gra

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>konika</mi><mo> </mo><mo>(</mo><mo>(</mo><mi>y</mi><mo>-</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>3</mn><mo>(</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>)</mo><mo>,</mo><mn>3</mn><mi>x</mi><mo>,</mo><mo> </mo><mn>2</mn><mi>sin</mi><mo> </mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo><mo>+</mo><mn>4</mn><mo> </mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra</mi><mo>=</mo><mi>marraztu</mi><mo> </mo><mo>(</mo><msub><mi>b</mi><mi>n</mi></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>n</mi><mo>≠</mo><mn>1</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>faltsu</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Martamatika Geometria Cloze a) 12 cm-ko altuerako laukizuzen bat 8 cm-ko altuera eta 3 cm-ko zabalera dituen beste baten antzekoa izan dadin, zabalera hau izango du: {#1} cm.

b) 30 km 2,5 cm giza adierazi nahi badugu, eskala hau erabili dugu: {#2}

c)Begiratu hurrengo irudia #iru

Eta kalkulatu x-ren luzeera: {#3} cm

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>geometria_egoera</mi><mfenced><mtext>"2D"</mtext></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iru</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>erakutsi_ardatzak</mtext><mo>(</mo><mo> </mo><mi>faltsu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>erakutsi_sarea</mi><mo>(</mo><mi>faltsu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="center"><mtr><mtd><mi>zentroa</mi><mo> </mo><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi><mo> </mo><mo>=</mo><mo> </mo><mn>30</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo> </mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>hiruki</mi><mo>(</mo><mi>puntu</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>cos</mi><mo> </mo><mi>β</mi><mo>)</mo><mo>,</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>sin</mi><mo> </mo><mi>β</mi><mo>)</mo></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>hiruki</mi><mo> </mo><mo>(</mo><mi>puntu</mi><mo> </mo><mo>(</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mi>puntu</mi><mo> </mo><mo>(</mo><mi>c</mi><mo>+</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mi>puntu</mi><mo> </mo><mo>(</mo><mi>m</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>cos</mi><mo> </mo><mi>β</mi><mo>)</mo><mo>)</mo><mo>+</mo><mn>8</mn><mo>,</mo><mi>m</mi><mo>*</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>sin</mi><mo> </mo><mi>β</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mo> </mo><mo>(</mo><mi>iru</mi><mo>,</mo><mi>H</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo> </mo><mtable align="center"><mtr><mtd><mi>bete</mi><mo>=</mo><mi>ziur</mi></mtd></mtr></mtable><mo>,</mo><mi>betetzeko_kolorea</mi><mo>=</mo><mi>gorria</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mfenced><mrow><mi>iru</mi><mo>,</mo><mi>I</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo> </mo><mtable align="center"><mtr><mtd><mi>bete</mi><mo>=</mo><mi>ziur</mi></mtd></mtr></mtable><mo>,</mo><mi>betetzeko_kolorea</mi><mo>=</mo><mi>berdea</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mo> </mo><mo>(</mo><mi>iru</mi><mo>,</mo><mi>segmentu</mi><mo>(</mo><mi>H</mi><mo>,</mo><mn>1</mn><mo> </mo><mo>)</mo><mo>,</mo><mo> </mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi><mo>,</mo><mo> </mo><mi>etiketa</mi><mo>=</mo><mi>b</mi><mo> </mo><mi>cm</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mo> </mo><mo>(</mo><mi>iru</mi><mo>,</mo><mi>segmentu</mi><mo>(</mo><mi>H</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mo> </mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi><mo>,</mo><mo> </mo><mi>etiketa</mi><mo>=</mo><mi>a</mi><mo> </mo><mi>cm</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mo> </mo><mo>(</mo><mi>iru</mi><mo>,</mo><mi>segmentu</mi><mo>(</mo><mi>I</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo> </mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi><mo>,</mo><mo> </mo><mi>etiketa</mi><mo>=</mo><mi>x</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu</mi><mo> </mo><mo>(</mo><mi>iru</mi><mo>,</mo><mi>segmentu</mi><mo>(</mo><mi>I</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mo> </mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi><mo>,</mo><mo> </mo><mi>etiketa</mi><mo>=</mo><mi>c</mi><mo> </mo><mi>cm</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Martamatika Geometria Ensayo 7 eta 5 cm-ko aldeko karratuak antzekoak al dira? Arrazoitu ONDO zure erantzuna.

]]> 1.0000000 0.0000000 0 editor 15 0 <question/> MONOMIOEN ARTEKO ERAGIKETAK Monomioen arteko batuketak eta kenketa

#a.x+#b.x+#a.y+#b.y

]]> ondo!

]]> 1.0000000 0.3333333 0 0 #erantzuna]]> Aurrera!

#graf

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #fx

]]> Oso ondo

]]> #f1x

]]> Kontuz, ondo fijatu grafikoan (gorakorra, beherakorra, y ardatzarekiko ebakitze puntua)

]]> #f2x

]]> Kontuz, ondo fijatu grafikoan (gorakorra, beherakorra, y ardatzarekiko ebakitze puntua)

]]> #f3x

]]> Kontuz, ondo fijatu grafikoan (gorakorra, beherakorra, y ardatzarekiko ebakitze puntua)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/mfrac»«mo»§#183;«/mo»«msup»«mfenced»«mrow»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msqrt»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«/mrow»«/mfrac»«/msqrt»«mo»§#183;«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»j«/mi»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»k«/mi»«/mrow»«/msup»«/math»

]]> Gogoratu eragiketen hierarkia eta ez ahaztu azken emaitza sinplifikatzea posible bada

]]> 1.0000000 0.1000000 0 0 #sol Oso ondo

]]> 1.0000000 0.1000000 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #g1

]]> #r1 #g2

]]> #r2 #g3

]]> #r3 #r4 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>;</mo><mi>T2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>;</mo><mi>T3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>·</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>·</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>,</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>:</mo><mo>=</mo><msub><mfenced><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>·</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>,</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>·</mo><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>r3</mi></mtd></mtr></mtable></mfenced></mrow></mfenced><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>T3</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>anchura_línea</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zuzen perpendikularrak «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Z«/mi»«mi»e«/mi»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»P«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»u«/mi»«mi»t«/mi»«mi»i«/mi»«mi»k«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»s«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»u«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»k«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»r«/mi»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»u«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»k«/mi»«mi»u«/mi»«mi»a«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mo»?«/mo»«/math»

]]> 1.0000000 0.1000000 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«/math»

]]> Oso ondo

]]> #r1

]]> #r2

]]> #r3

#a . ( #b) . (#c) = 0

]]> 1.0000000 0.3333333 0 0 #s <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo> </mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>ebatz</mi><mfenced><mrow><mi>abc</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 2. mailako funtzioen grafikoa2 Ondoko adierazpen hauetako zein dagokio azpiko grafikoari?

]]> Gogoratu nola egiten den funtzioen traslazioa. Begiratu liburuan!

]]> 1.0000000 0.1000000 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #e1

]]> Ederto!

]]> #e2

]]> Hurrengo saiakeran begiratu ondo parabolaren erpinaren koordenatu biren balioak zeintzuk diren.

]]> #e3

]]> Hurrengo saiakeran begiratu ondo parabolaren erpinaren koordenatu biren balioak zeintzuk diren.

]]> #e4

]]> Parabolaren erpinaren koordenatuaz gain "a" koefizientearen ikurra begiratu behar duzu, ahurra ala ganbila den ziurtatzeko.

]]> #e5

]]> Hurrengo saiakeran begiratu ondo parabolaren erpinaren koordenatu biren balioak zeintzuk diren.

]]> #e6

]]> Hurrengo saiakeran begiratu ondo parabolaren erpinaren koordenatu biren balioak zeintzuk diren.

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>∈</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mo>-</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e5</mi><mo>=</mo><mo>-</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e6</mi><mo>=</mo><mo>-</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 2. mailako funtzioen grafikoak #g grafikoa f(x)=#i funtzioari dagokio?

]]> Gogoratu!! Parabolaren erpina x=-b/(2a) abzisadun puntuan dagoela eta x-ren balio honi dagokion ordenatuaren balioa y(x), x-ren balioa y-ren adierazpenean ordezkatuz lortzen da.

]]> 1.0000000 1.0000000 0 Verdadero Ederto! Bere erpina (#d,#e) puntuan baitu.

]]> Falso Kontuz! Begiratu ea parabolaren erpinaren koordenatuak ondo lortu dituzun.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">variables</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>,</mo><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi><mo>+</mo><mi>m</mi></mrow></mfenced><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>+</mo><mi>m</mi><mo>)</mo><mo>,</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>+</mo><mi>m</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>h</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>h</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>h</mi><mo>=</mo><mi>i</mi><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>12</mn><mo>,</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 2. mailako futzioen traslazioa Lotu itzazu ondoko grafikoak dagokion funtzioaren adierazpenarekin

]]> 1.0000000 0.1000000 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #g1

]]> #e1 #g2

]]> #e2 #g3

]]> #e3 #g4

]]> #e4 #g5

]]> #e5 #g6

]]> #e6 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s5</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s6</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>∈</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>^</mo><mn>2</mn><mo>+</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>^</mo><mn>2</mn><mo>+</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>e2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>^</mo><mn>2</mn><mo>+</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>e3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>^</mo><mn>2</mn><mo>+</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mi>e4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e5</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>^</mo><mn>2</mn><mo>+</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g5</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s5</mi><mo>,</mo><mi>e5</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e6</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>^</mo><mn>2</mn><mo>-</mo><mi>b</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g6</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s6</mi><mo>,</mo><mi>e6</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 3. mailako polinomioren faktorizazioa. Deskonposa ezazu ondoko polinomioa lehenengo mailako monomioetan Ruffiniren erregela erabiliz:

#pol

]]> Gogoratu polinomioa Ruffini bidez faktorizatzeko gai askearen zatitzaile guztiekin frogatu beharko duzula. ANIMO!

]]> 1.0000000 0.1000000 0 0 #sol EDERTO!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>faktorizatu</mi><mo>(</mo><mi>pol</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ebatz</mi><mfenced><mrow><mi>pol</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Adierazpen Grafikoa1 Ondorengo adierazpen grafikoa f(x) = #h funtzioari dagokio?

DEFINIZIO-EREMUA	{#1}{#2}
IBILBIDEA	{#3}
ASINTOTA HORIZONTALA	y= {#4}
ASINTOTA BERTIKALA	x= {#5}
SIMETRIA
ADIERAZPEN ALJEBRAIKOA

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«mo»§#8594;«/mo»«/mover»«mo»+«/mo»«mover»«mrow»«mi»B«/mi»«mi»C«/mi»«/mrow»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«/math»{#1}

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mrow»«mi»O«/mi»«mi»B«/mi»«/mrow»«mo»§#8594;«/mo»«/mover»«mo»+«/mo»«mover»«mrow»«mi»O«/mi»«mi»C«/mi»«/mrow»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«/math»{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>geometria_egoera</mi><mfenced><mtext>"2D"</mtext></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>;</mo><mi>B</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>;</mo><mi>C</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>;</mo><mi>D</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>)</mo><mo>;</mo><mi>O</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>segmentu</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></mfenced><mo>;</mo><mi>s</mi><mo>=</mo><mi>segmentu</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>C</mi></mrow></mfenced><mo>;</mo><mi>t</mi><mo>=</mo><mi>segmentu</mi><mfenced><mrow><mi>C</mi><mo>,</mo><mi>D</mi></mrow></mfenced><mo>;</mo><mi>q</mi><mo>=</mo><mi>segmentu</mi><mfenced><mrow><mi>D</mi><mo>,</mo><mi>A</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>10</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>w</mi><mo>,</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>q</mi><mo>}</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>w</mi><mo>,</mo><mo>{</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>O</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi><mo>}</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Bigarren mailako ekuazioak Ebatzi ekuazioa hau #E

]]> Animo !!

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo> </mo><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Bigarren mailako polinomioak faktorizatu Faktorizatu hurrengo polinomioa: P(x)=#P

]]> 1.0000000 0.2000000 0 0 #fakt Primeran!

A:{puntuen batura 5 da}

B:{dado batean 4 atera dugu}

C:{Bi dadoen emaitza bera lortu dugu}

Idatzi A,B eta C-en oinarrizko gertaerak eta kalkulatu bakoitzaren probabilitateak.

]]> Kontuan izan bi dado botatzen ditugunean, lagin-espazioan 36 elementu daudela.

]]> 1.0000000 0.0000000 0 editor 15 0 <question/> Datuen antolaketa Ikastetxe bateko DBHko 4. mailako ikasleei galdetuta zenbat gastatzen duten urteko zinera joaten (sarrerak, palomitak eta abarrekoak sarturik) hauek izan dira erantzunak:

105	80	90	100	120	80	40	50	90	110
50	60	110	100	90	40	100	110	40	100
70	80	80	90	110	100	90	200	80	50
50	80	100	110	100	90	110	150	200	80
30	100	120	100	120	90	90	80	110	100
50	110	110	120	130	180	90	90	70	80
90	80	90	80	100	130	80	110	130	100
100	110	100	90	70	50	180	100	110	100

Antolatu datu hauek taula estatistiko batean eta kalkulatu banaketa neurririk garrantzitsuenak.

Behin lortuta datu horiek komentau ea logikoak iruditzen zaizkizun eta zergatik.

]]> 1.0000000 0.0000000 0 editor 30 0

TARTEAK

KOPURUA

MAIZTASUNA

…..

]]> <question/> DefinizioEremua1 Zein da f(x)=#h funtzioaren definizio eremua?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #eremu1

]]> #eremu2

]]> #eremu3

#ek

OHARRA:
Adierazi emaitza era honetara , adibidez: { { x =3} }

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ek</mi><mo>=</mo><msqrt><mrow><mi>a</mi><mo> </mo><mo>·</mo><mo> </mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></msqrt><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ebatz</mi><mfenced><mrow><mi>ek</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ekuazio Irrazionalak Ondorengo ekuazioa ebatzi:

#ek

Oharra: Wiris editorea erabili emaitza zatiki moduan adierazteko.

]]> Ongi pentsatu erroa kentzeko eman beharreko pausuak.

]]> 1.0000000 0.2500000 0 0 #Em Primeran! Hurrengo batekin animatzen?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c2«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»#a21«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b21«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c21«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a22«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b22«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c22«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»#a31«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b31«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c31«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a32«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b32«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c32«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»#a41«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b41«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c41«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a42«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b42«/mi»«mo»·«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#c42«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mtd»«/mtr»«/mtable»«/math»

]]> 1.0000000 0.1000000 0 true Soluzioa P=#P da eta grafikoak: #t1 dira.

]]> {#a1·x+#b1·y=#c1 ; #a2·x+#b2·y=#c2 Soluazioa ondokoa da :Q=#Q eta grafikoa berriz: #t2

]]> {#a21·x+#b21·y=#c21 ; #a22·x+#b22·y=#c22 Sistemaren grafikoak zuzen berdinak dira. Lerro gorria lodiagoa da zuzen bat bestearen gainean dagoela ikusteko. Grafikoak ondokoak dira: #t3

]]> {#a31·x+#b31·y=#c31 ; #a32·x+#b32·y=#c32 Sistemaren grafikoak zuzen paraleloak dira. Ondokoak dira: #t4

]]> {#a41·x+#b41·y=#c41 ; #a42·x+#b42·y=#c42 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>21</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>·</mo><mi>s1</mi><mo>+</mo><mi>b1</mi><mo>·</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>·</mo><mi>s1</mi><mo>+</mo><mi>b2</mi><mo>·</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mfrac><mi>a1</mi><mi>a2</mi></mfrac></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mfrac><mi>b1</mi><mi>b2</mi></mfrac></mtd></mtr></mtable><mrow><mi>p1</mi><mo>≠</mo><mi>p2</mi><mo>∧</mo><mi>a1</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b1</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c1</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b2</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c2</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c1</mi><mo>-</mo><mi>a1</mi><mo>·</mo><mi>x</mi></mrow><mi>b1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f12</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>-</mo><mi>a2</mi><mo>·</mo><mi>x</mi></mrow><mi>b2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mi>f11</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g12</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mi>f12</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>berdea</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g13</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mi>P</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>,</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>5</mn><mo>,</mo><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>21</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>s21</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s22</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b21</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c21</mi><mo>=</mo><mi>a21</mi><mo>·</mo><mi>s21</mi><mo>+</mo><mi>b21</mi><mo>·</mo><mi>s22</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b22</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c22</mi><mo>=</mo><mi>a22</mi><mo>·</mo><mi>s21</mi><mo>+</mo><mi>b22</mi><mo>·</mo><mi>s22</mi></mtd></mtr><mtr><mtd><mi>p21</mi><mo>=</mo><mfrac><mi>a21</mi><mi>a22</mi></mfrac></mtd></mtr><mtr><mtd><mi>p22</mi><mo>=</mo><mfrac><mi>b21</mi><mi>b22</mi></mfrac></mtd></mtr></mtable><mrow><mi>p21</mi><mo>≠</mo><mi>p22</mi><mo>∧</mo><mi>a21</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b21</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c21</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a22</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b22</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f21</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c21</mi><mo>-</mo><mi>a21</mi><mo>·</mo><mi>x</mi></mrow><mi>b21</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f22</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c22</mi><mo>-</mo><mi>a22</mi><mo>·</mo><mi>x</mi></mrow><mi>b22</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g21</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t2</mi><mo>,</mo><mi>f21</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g22</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t2</mi><mo>,</mo><mi>f22</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>berdea</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>s21</mi><mo>,</mo><mi>s22</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g23</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t2</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>,</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>5</mn><mo>,</mo><mi>erakutsi_etiketa</mi><mo>=</mo><mi>ziur</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>21</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m3</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a31</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b31</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c31</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a32</mi><mo>=</mo><mi>m3</mi><mo>*</mo><mi>a31</mi></mtd></mtr><mtr><mtd><mi>b32</mi><mo>=</mo><mi>m3</mi><mo>*</mo><mi>b31</mi></mtd></mtr><mtr><mtd><mi>c32</mi><mo>=</mo><mi>m3</mi><mo>·</mo><mi>c31</mi></mtd></mtr><mtr><mtd><mi>p31</mi><mo>=</mo><mfrac><mi>c31</mi><mi>b31</mi></mfrac></mtd></mtr><mtr><mtd><mi>p32</mi><mo>=</mo><mfrac><mi>c32</mi><mi>b32</mi></mfrac></mtd></mtr><mtr><mtd><mi>dif</mi><mo>=</mo><mi>p31</mi><mo>-</mo><mi>p32</mi></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mi>dif</mi></mfenced><mo>⩾</mo><mn>2</mn><mo>∧</mo><mi>m3</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mfenced close="|" open="|"><mi>dif</mi></mfenced><mo>⩾</mo><mn>2</mn><mo>∨</mo><mfenced close="|" open="|"><mi>p31</mi></mfenced><mo>⩽</mo><mn>10</mn><mo>∧</mo><mfenced close="|" open="|"><mi>p32</mi></mfenced><mo>⩽</mo><mn>10</mn><mo>∧</mo><mi>a31</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b31</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c31</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a32</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b32</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c32</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f31</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c31</mi><mo>-</mo><mi>a31</mi><mo>·</mo><mi>x</mi></mrow><mi>b31</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f32</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c32</mi><mo>-</mo><mi>a32</mi><mo>·</mo><mi>x</mi></mrow><mi>b32</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g31</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t3</mi><mo>,</mo><mi>f31</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g32</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t3</mi><mo>,</mo><mi>f32</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>berdea</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>21</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m4</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a41</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b41</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c41</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a42</mi><mo>=</mo><mi>m4</mi><mo>*</mo><mi>a41</mi></mtd></mtr><mtr><mtd><mi>b42</mi><mo>=</mo><mi>m4</mi><mo>*</mo><mi>b41</mi></mtd></mtr><mtr><mtd><mi>m5</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c42</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>ord1</mi><mo>=</mo><mfrac><mi>c41</mi><mi>b41</mi></mfrac></mtd></mtr><mtr><mtd><mi>ord2</mi><mo>=</mo><mfrac><mi>c42</mi><mi>b42</mi></mfrac></mtd></mtr><mtr><mtd><mi>diford</mi><mo>=</mo><mfrac><mi>ord2</mi><mi>ord1</mi></mfrac></mtd></mtr><mtr><mtd><mi>diford2</mi><mo>=</mo><mi>ord2</mi><mo>-</mo><mi>ord1</mi></mtd></mtr></mtable><mrow><mi>b41</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>b42</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mfenced close="|" open="|"><mi>ord1</mi></mfenced><mo>⩽</mo><mn>10</mn><mo>∧</mo><mfenced close="|" open="|"><mi>ord2</mi></mfenced><mo>⩽</mo><mn>10</mn><mo>∧</mo><mfenced close="|" open="|"><mi>diford2</mi></mfenced><mo>⩾</mo><mn>2</mn><mo>∧</mo><mfenced close="|" open="|"><mi>diford</mi></mfenced><mo>≠</mo><mi>m4</mi><mo>∧</mo><mi>m4</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a41</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c41</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a42</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f41</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c41</mi><mo>-</mo><mi>a41</mi><mo>·</mo><mi>x</mi></mrow><mi>b41</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f42</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>c42</mi><mo>-</mo><mi>a42</mi><mo>·</mo><mi>x</mi></mrow><mi>b42</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g41</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t4</mi><mo>,</mo><mi>f41</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g42</mi><mo>=</mo><mi>marraztu</mi><mfenced><mrow><mi>t4</mi><mo>,</mo><mi>f42</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>kolorea</mi><mo>=</mo><mi>berdea</mi><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>,</mo><mn>6</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f12</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>31</mn><mn>10</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>79</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>10</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ekuazioak Ebatzi ekuazio hau #F

]]> Kontuan izan ekuazio batzuk ez dutela soluziorik

]]> 1.0000000 0.1000000 0 0 #sol Zorionak!!!

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #t1

]]> #sol1 #t2

]]> #sol2 #t3

]]> #sol3 #t4

]]> #sol4 #sol5 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mo> </mo><mi>s2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mo> </mo><mi>s3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mo> </mo><mi>s4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mo>(</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>sol1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>sol2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>sol3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mi>sol4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi><mo>=</mo><mo>(</mo><mi>a4</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b4</mi><mo>+</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi><mo>,</mo><mi>sol4</mi><mo>,</mo><mi>sol5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>,</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Errodun funtzioen definizio-eremua Zein da f(x)=#fx funtzioaren definizio-eremua?

]]> 1.0000000 0.3333333 0 true true none Primeran!

]]> Akatsak zuzendu...

Pentsatu: zer baldintza bete behar du balio batek bere erroa kalkulatu ahal izateko?

]]> Berriz ere saiatu.

Gogoratu: errokizun negatibodun erroak ezin ditugu kalkulatu. Beraz, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/msqrt»«/math»dugunean, x-ren zein balioentzat «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8805;«/mo»«mn»0«/mn»«/math» betetzen den ikusiko dugu.

]]> #dom1

]]> #dom2

]]> #dom3

]]> #dom4

]]> 1.0000000 0.3333333 0 true true none Primeran!

]]> Akatsak zuzendu...

Pentsatu: zer baldintza bete behar du balio batek bere erroa kalkulatu ahal izateko?

]]> Berriz ere saiatu.

Gogoratu: errokizun negatibodun erroak ezin ditugu kalkulatu. Beraz, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/msqrt»«/math»dugunean, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8805;«/mo»«mn»0«/mn»«/math» x-ren zein balioentzat betetzen den ikusiko dugu.

]]> #dom1

]]> Primeran!!

]]> #dom2

]]> #dom3

]]> #dom4

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fx</mi><mo>=</mo><msqrt><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dom1</mi><mo>=</mo><mi>eremua</mi><mo>(</mo><msqrt><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dom2</mi><mo>=</mo><mi>eremua</mi><mo>(</mo><msqrt><mrow><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dom3</mi><mo>=</mo><mi>eremua</mi><mo>(</mo><msqrt><mrow><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dom4</mi><mo>=</mo><mi>eremua</mi><mo>(</mo><msqrt><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msqrt><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dom1</mi><mo>,</mo><mo> </mo><mi>dom2</mi><mo>,</mo><mo> </mo><mi>dom3</mi><mo>,</mo><mo> </mo><mi>dom4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>⩽</mo><mi>x</mi><mo>⩽</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>∨</mo><mi>x</mi><mo>⩽</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>,</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn><mo>⩽</mo><mi>x</mi><mo>⩽</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>1</mn><mo>⩽</mo><mi>x</mi><mo>⩽</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Eskola p(ezA eta ezB)

Eskola bateko #a ikasletatik, #c-k Euskera gainditzen dute, #s-k Gaztelania eta #cs-k irakasgai biak gainditzen dituzte. Kalkulatu ikasle bat zoriz aukeratuta, irakasgai biak suspeditu dituen bat izateko probabilitea.

Hurbildu emaitza bi hamartarretara

]]> 1.0000000 0.5000000 0 0 #p <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerantzia_erlatiboa</mi><mo>(</mo><mi>faltsu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>perdoi_o_tolerantzia</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>005</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>300</mn><mo>.</mo><mo>.</mo><mn>700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>400</mn><mo>.</mo><mo>.</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cs</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mi>min</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>s</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>s</mi><mo>-</mo><mi>cs</mi><mo>+</mo><mi>ausazko</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>s</mi><mo>-</mo><mi>cs</mi></mrow><mi>a</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>487</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>416</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>223</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>938</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.28</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><correctAnswers><correctAnswer>#p</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Funtzio baten adierazpen grafikoa f(x)=#h funtzioari honako grafiko hau al dagokio?

]]> 1.0000000 1.0000000 0 Verdadero Oso ondo!!!!

]]> Falso Ez duzu asmatu!!!!

]]> 1.0000000 0.1000000 0 true true abc (#q)

]]> #i1

]]> #i2

]]> (#i3)

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msqrt><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>-</mo><pi/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>d</mi><mo>,</mo><mi>j</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>cosec</mi><mo>(</mo><mi>c</mi><mo>/</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sin</mi><mo>(</mo><mi>asin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>p1</mi><mo>,</mo><mi>p2</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mn>2</mn><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>-</mo><mi>c</mi><mo>/</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>f</mi><mo>=</mo><mi>d</mi><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>h</mi><mo>=</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>q</mi><mo>=</mo><mo>(</mo><mi>t1</mi><mo>,</mo><cn>+∞</cn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i1</mi><mo>=</mo><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><reals/></mtd></mtr><mtr><mtd><mi>i3</mi><mo>=</mo><mo>(</mo><cn>-∞</cn><mo>,</mo><mi>t1</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>f</mi><mo>=</mo><mi>d</mi><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>h</mi><mo>=</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>q</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>,</mo><cn>+∞</cn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>i1</mi><mo>=</mo><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><reals/></mtd></mtr><mtr><mtd><mi>i3</mi><mo>=</mo><mo>(</mo><cn>-∞</cn><mo>,</mo><mi>t1</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>f</mi><mo>=</mo><mi>j</mi><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>h</mi><mo>=</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>q</mi><mo>=</mo><mo>(</mo><pi/><mo>,</mo><cn>+∞</cn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i1</mi><mo>=</mo><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><pi/></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><reals/><mo>-</mo><mo>{</mo><mn>0</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>i3</mi><mo>=</mo><mo>(</mo><mo>-</mo><pi/><mo>,</mo><cn>+∞</cn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>f</mi><mo>=</mo><mi>j</mi><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>h</mi><mo>=</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>q</mi><mo>=</mo><mo>(</mo><pi/><mo>,</mo><cn>+∞</cn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i1</mi><mo>=</mo><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><pi/></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><reals/><mo>-</mo><mo>{</mo><mn>0</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>i3</mi><mo>=</mo><mo>(</mo><mo>-</mo><pi/><mo>,</mo><cn>+∞</cn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mi>f</mi><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><reals/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><cn>+∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzio baten jarraitasuna Funtzio bakoitzeko esan jarraia ala etena den eta etena bada, eten mota.

]]> 1.0000000 0.1000000 0 true #A1

]]> Essential discontinuity #B1

]]> Removable discontinuity #C1

]]> Jauzia #D1

]]> Jarraia <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mfrac><mn>2</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tA</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>tA</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tB</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>1</mn><mo>.</mo><mn>99</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mo>(</mo><mn>2</mn><mo>.</mo><mn>01</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b5</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>30</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>puntu</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>,</mo><mo>{</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>txuri</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>tB</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>,</mo><mi>b5</mi><mo>,</mo><mi>b4</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tC</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>tC</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tD</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>tD</mi><mo>,</mo><mi>s5</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzio esponentzialak Lotu funtzio esponentzial bakoitza dagokion adierazpen analitikoarekin.

Oharra: Aukeretan f(x)= e^(x-2) - 1 agertzen denean, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»e«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«/mstyle»«/math» ulertuko dugu.

]]> 1.0000000 0.2500000 0 true Primeran!

]]> Akatsak zuzendu...

Gogoratu: f(x)=e^x+a+ b funtzioan, b koefizienteak asintota horizontala zein duen adierazten digu; hau da, oinarriko funtzioa goruntz (+b) edo beheruntz (-b) zenbat unitate desplazatu den.

]]> Berriz ere saiatu!

Gogoratu: f(x)=e^x+a + b funtzioa izanik

b koefizienteak asintota horizontala zein duen adierazten digu; hau da, oinarriko funtzioa goruntz (+b) edo beheruntz (-b) zenbat unitate desplazatu den.
a koefizienteak oinarriko funtzioa eskubiruntz (-a) edo ezkerreruntz (+a) zenbat unitate desplazatu den adierazten digu. [ikus oinarrizko funtzioaren (0,1) puntu esanguratsuaren desplazamendua].

]]> #g1

]]> f(x)= #f1 #g2

]]> f(x)= #f2 #g3

]]> f(x)= #f3 f(x)= #f4 f(x)= #f5 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>exp</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></msup><mo>+</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mi>c3</mi></mrow></msup><mo>+</mo><mi>d3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mi>c4</mi></mrow></msup><mo>+</mo><mi>d4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mi>c5</mi></mrow></msup><mo>+</mo><mi>d5</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mi>x</mi></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msup><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzio kuadratikoa Lotu parabola bakoitza dagokion adierazpen analitikoarekin.

Oharra: Erantzunetan x^2 dagoen lekuan x² ulertu behar da.

]]> 1.0000000 0.2500000 0 true Primeran!

]]> Akatsak zuzendu...

Gogoratu: a koefizientea positiboa bada parabolaren adarrak goruntz begira egongo dira, eta negatiboa bada, berriz, beheruntz.

]]> Berriz ere saiatu!

Gogoratu:

a koefizientea positiboa bada parabolaren adarrak goruntz begira egongo dira, eta negatiboa bada, berriz, beheruntz.
parabola osatzen duten puntuek adierazpen analitikoaren berdintza bete behar dute: (0, c) puntua

]]> #g1

]]> f(x)= #f1 #g2

]]> f(x)= #f2 #g3

]]> f(x)= #f3 f(x)= #f4 f(x)= #f5 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo><mi>s3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>b3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>c3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mi>b4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>c4</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c5</mi><mo>=</mo><mi>a5</mi><mo>*</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>c5</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d5</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d5</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzio linealak: grafikoa ekuazioarekin erlazionatu Grafikoan azaltzen den funtzioa dagokion ekuazioarekin elkartu:

#graf

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> Oso ongi. Zorionak. Jarraitu praktikatzen]]> #sol2

]]> Ez duzu asmatu. Jarraitu praktikatzen]]> #sol3

]]> Ez duzu asmatu. Jarraitu praktikatzen]]> #sol4

]]> Ez duzu asmatu. Jarraitu praktikatzen]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi><mo>,</mo><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzioak eta grafikoak bat al datoz Grafikoan azaltzen den funtzioa, f(x)=#h funtzioaren adierazpena al da?

]]> 1.0000000 1.0000000 0 Verdadero Oso ondo, jarraitu beste batekin!

]]> Falso Ez duzu asmatu. Saiatu beste batekin!

]]> 1.0000000 1.0000000 0 Verdadero Izan beti gogoan funtzio mota bakoitzaren ezaugarriak.

]]> Falso Izan beti gogoan funtzio mota bakoitzaren ezaugarriak.

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><msup><exponentiale/><mi>x</mi></msup><mo>,</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>,</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>,</mo><mi>ln</mi><mo> </mo><mi>x</mi><mo>,</mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>,</mo><mi>cos</mi><mo> </mo><mi>x</mi><mo>}</mo><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>f</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>g</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>g</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mi>g</mi><mo>=</mo><mi>h</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>ziur</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Galton-en aparatua Galton-en aparatua bola bat tope baten kontra talka egin ostean eskumara edo ezkerrera desplazatzen duen mekanismo bat da. Bola behin eta berriz tope batekin talka egin eta eskuma edo ezkerrera desplazatzen da azkenean gelaxka batean jausi arte.

Aztertu honako irudia eta jarrai ezazu bertan agertzen diren jarraibideak esperimentua askotan eginez:

Egin esperimentua 100 aldiz (F9-ri ehun aldiz sakatuz) eta ikusi zer gertatzen den.

Ondoren, kalkula ezazu bolak gelaxka bakoitzean jausteko probabilitatea zein den.

]]> 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1.0000000 0.0000000 0 editor 15 0 <question/> Grafikoak Ondorengo grafikoak ematen digun informazioa laburki azaldu, tarte bakoitzean ematen den abiadura zehaztuz. Grafiko hori izan dezakeen adibide bat asmatu.

Grafikoa

]]> 1.0000000 0.0000000 0 editor 20 0 <question/> Inecuaciones. Inecuación de 2º grado. Respuesta Corta.

Escribe la solución de la inecuación de 2º grado, siguiendo la notación siguiente:

Si la solución es un único intervalo, éste se debe escribir utilizando el símbolo &. Puedes seguir el ejemplo siguiente: x>3&x<8
Si la solución son dos intervalos separados, debes utilizar el símbolo | que se obtiene pulsando Alt Gr y el 1 a la vez. Por ejemplo: x<1|x>5.
Si no tiene solución, debes escribir falso.
El símbolo mayor o igual se debe escribir >=.
El símbolo menor o igual se escribirá <=.
La fracción se debe escribir con el símbolo /.
Si fuera negativa la fracción pondremos un - delante del numerador.

]]> 1.0000000 0.1000000 0 0 #ss <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>s1</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>s2</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>i</mi><mo>&lt;</mo><mn>0</mn><mo>,</mo><mi>i</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>i</mi><mo>&les;</mo><mn>0</mn><mo>,</mo><mi>i</mi><mo>&ges;</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>s</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&ges;</mo><mo>-</mo><mn>6</mn><mo>&amp;</mo><mi>x</mi><mo>&les;</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #ss </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> kuboa Zenbat aurpegi ditu kubo batek erpin berean?{#1}

Zenbat aurpegiri egiten diote komun ertz bakoitzak kubo batean?{#2}

]]> Kontuan izan kubo batek sei aurpegi dituela!!!!

#enun

Pauso guztiak azaldu behar dituzu, bata bestearen azpiko lerroan idatziz.

]]> Berriz ere saiatu! Animo!

]]> 1.0000000 0.3333333 0 0 #sol Primeran!!!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ebatz</mi><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mi>a1</mi></mrow><mrow><mn>2</mn><mi>b</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>x</mi></mrow><mi>b</mi></mfrac><mo>=</mo><mi>a3</mi><mo>-</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mi>a4</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a5</mi></mrow></mfenced></mrow><mi>c</mi></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enun</mi><mo>=</mo><mi>katea_ordeztu</mi><mfenced><mrow><mo>"</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>8</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mo>#</mo><mn>2</mn><mo>+</mo><mi>x</mi></mrow><mrow><mo>#</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mo>#</mo><mn>3</mn><mo>-</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mo>#</mo><mn>4</mn><mi>x</mi><mo>-</mo><mo>#</mo><mn>5</mn></mrow></mfenced></mrow><mrow><mo>#</mo><mn>7</mn></mrow></mfrac><mo>"</mo><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mn>2</mn><mi>b</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enun</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>6</mn></mrow><mn>14</mn></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mi>x</mi></mrow><mn>7</mn></mfrac><mo>=</mo><mn>5</mn><mo>-</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>6</mn></mrow></mfenced></mrow><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>331</mn><mn>105</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Lotu grafikoa eta adierazpen analitikoa Ondoko grafikoa funtzio honi dagokio f(x)=#h?

( #p1 ) * ( #p2 ) =

OHARRA: a xⁿ horrela idatzi dezakezu: a * x ^ n

]]> Saiatu zaitez berriz!!!

]]> 1.0000000 0.1000000 0 0 #sol Oso ongi, jarraitu horrela!!!

]]> 1.0000000 0.3333333 0 true true abc Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> #d1

]]> OSO ONDO !!!

]]> #d2

]]> #d3

]]> #d4

]]> #d5

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo><mo>*</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Parabolak eta erpinak Ondoko adierazpen analitikoa f(x)=#g duen parabolaren erpina beheko abszisan dago?

]]> Animo!!

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>f</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>g</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mi>g</mi><mo>=</mo><mi>h</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Polinomio baten deribatua eta bere adierazpen grafikoa Funtzio polinomiko honetan «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math»#f, idatzi bere deribatua {#1} eta jarri ezazu zein den funtzioaren grafikoa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» {#2}.]]> 2.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>12</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>tablero</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>12</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>tablero</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>anchura</mi><mo>=</mo><mn>12</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mo>*</mo><msup><mi>x</mi><mrow><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>f</mi><mo>:=</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>m</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>grado</mi><mfenced><mi>f</mi></mfenced><mo>&gt;</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>f</mi><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>t1</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>t2</mi><mo>,</mo><mi>g</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>t3</mi><mo>,</mo><mi>g</mi><mo>&apos;</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Polinomioak1 Faktoriza ezazu ondorengo polinomioa:

#poli

]]> 1.0000000 0.1000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli</mi><mo>:</mo><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>faktorizatu</mi><mo>(</mo><mi>poli</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="times_operator">·</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Polinomioen faktorizazioa P(x)= #P polinomioari ondorengo faktorizazioa dagokio: #fakt

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fakt</mi><mo>=</mo><mi>faktorizatu</mi><mo>(</mo><mi>P</mi><mo>,</mo><integers/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>em</mi><mo>:=</mo><mo>(</mo><mi>P</mi><mo>=</mo><mi>fakt</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>,</mo><mi>fakt</mi><mo>,</mo><mi>em</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mi>faltsu</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Puntuen koordenatuak Esan ezazu zeintzuk diren irudi honetan azaltzen diren puntuaren koordenatuak: #fig

Idatzi ezazu erantzuna parentesi artean eta koordenatuak komaz bananduta)

{#1}

]]> 1.0000000 0.3333333 0 Oso ongi, asmatu duzu!}]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fig</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> RUFFINIREN ZATIKETA (ZATIKIZKOAK) P = #p y Q = #q. Kalkulatu polinomioen arteko zatiketa eta idatzi zein den C eta R :

C: ZATIDURA P : Q
R: HONDARRA P : Q

]]> Aurrera!

]]> 1.0000000 0.1000000 0 0 C=#CR=#R]]> Zorionak!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>)</mo></mrow><mrow><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mrow><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>q</mi><mo>:</mo><mo>=</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>gradu</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><msub><mi>q</mi><mrow><mi>gradu</mi><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msub><mo>=</mo><mn>1</mn><mo>∧</mo><msub><mi>q</mi><mn>0</mn></msub><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>p</mi><mo>:</mo><mo>=</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>gradu</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>⩾</mo><mi>gradu</mi><mo>(</mo><mi>q</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>:</mo><mo>=</mo><mi>zatidura</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>:</mo><mo>=</mo><mi>hondar</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>31</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>159</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>793</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3965</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>#</mo><mi>C</mi><mspace linebreak="newline"/><mi>R</mi><mo>=</mo><mo>#</mo><mi>R</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Trigonometria problema

Behatu irudiari eta ondoko datuei:

DISTANTZIA: a= #a metro

ANGELUA : A= #b radian

ANGELUA: B= #c radian

Kalkulatu c distantziaren luzera

Trigonometría

Aukeratu erantzun zuzena:

{#1}

]]> 1.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><pi/><mn>4</mn></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><pi/><mn>4</mn></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfrac><mrow><mi>tan</mi><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mrow><mi>tan</mi><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mfrac></mtd></mtr></mtable><mrow><mi>y</mi><mo><</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>tan</mi><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>-</mo><mi>y</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>d</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>d</mi><mo>+</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>d</mi><mo>+</mo><mn>7</mn></mtd></mtr></mtable></math></input></command></group></library></session> ]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Tuerka baten bolumena Nola kalkulatuko zenduke tuerka baten bolumena? Zein gorputz geometriko da? Esplika itzazu hitz gutxitan zeintzuk izango lirateke eman beharreko pausuak:

]]> 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 1.0000000 0.0000000 0 editor 15 0 <question/> Zatiki aljebraikoen sinplifikazioa Sinplifikatu ondoko zatiki aljebraikoa

#enun

]]> 1.0000000 0.1000000 0 0 #sol Oso ondo

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak_1</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>errepikatu</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo> </mo><mi>arte</mi><mo> </mo><mi>c</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi></mrow></mfenced><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enun</mi><mo>=</mo><mi>katea_ordeztu</mi><mfenced><mrow><mo>"</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>"</mo><mo>,</mo><mi>n</mi><mo>,</mo><mi>d</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n</mi><mi>d</mi></mfrac></math></input></command></group></library></session> ]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Zuzen baten malda «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«mo»+«/mo»«mi»m«/mi»«mo»-«/mo»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«/math» zuzena izanik, kalkulatu m-ren balioa ondorengoa bete dadin:

a) Zuzena (1, -2) puntutik igarotzen da. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«/math»{#1}

b) Zuzena «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«mn»3«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«mn»2«/mn»«/mfrac»«/math» zuzenarekiko perpendikularra da. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«/math»{#2}

]]> 3.0000000 0.3333333 0 <question><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zuzen baten zuzen ortogonala puntu batean Zein da zuzen honen #r zuzen ortogonala «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»=«/mo»«mi»#p«/mi»«/math» puntutik pasatzen dena? #q ]]> 1.0000000 0.1000000 0 0 #s <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo> </mo><mo>∧</mo><mo> </mo><mi>b</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>line</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>p</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mi>random</mi><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>p</mi><mo>∩</mo><mi>r</mi><mo>==</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>perpendicular</mi><mfenced><mrow><mi>r</mi><mo>,</mo><mi>p</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>p</mi><mo>,</mo><mo>{</mo><mi>label</mi><mo>=</mo><mi>p</mi><mo>,</mo><mo> </mo><mi>show_label</mi><mo>=</mo><mi>true</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>13</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #s </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">add</data><data name="casSession"><session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></data></localData></question> Zuzen eta parabolaren arteko ebaki-puntua Kalkulatu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»:«/mo»«/math»#f eta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»:«/mo»«/math»#g funtzioen arteko ebakidura puntuak.

Oharra: Emaitzak adierazteko modua:

Bi ebaki-puntu ditugunean: (balioa,balioa) eta (balioa,balioa)
Ebaki-puntu bakarra dugunean: (balioa,balioa) eta (Q)
Ebaki-punturik ez badago: (P) eta (Q)

]]> 1.0000000 0.3333333 0 0 (#P) eta (#Q)]]> Primeran!!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>em</mi><mo>=</mo><mi>ebatz</mi><mfenced><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>f</mi><mo>(</mo><msub><mi>em</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>f</mi><mo>(</mo><msub><mi>em</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mo>(</mo><msub><mi>em</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>(</mo><msub><mi>em</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>em</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><msqrt><mn>7</mn></msqrt></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><msqrt><mn>7</mn></msqrt></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msqrt><mn>7</mn></msqrt><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><msqrt><mn>7</mn></msqrt><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>7</mn></msqrt><mo>,</mo><mn>3</mn><mo>*</mo><msqrt><mn>7</mn></msqrt><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><mi>P</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>t</mi><mi>a</mi><mo> </mo><mo>(</mo><mo>#</mo><mi>Q</mi><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Zuzen ukitzailea Kalkulatu«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»#f funtzioaren zuzen ukitzailearen ekuazioa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mi»#p«/mi»«/math» puntuan. #dib ]]> 1.0000000 0.1000000 0 0 #r #f Funtzio bera jarri duzu!! Saiatu berriro...

]]> <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo> </mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><pi/><mo>*</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>p</mi><mo>,</mo><mi>g</mi><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>q</mi><mo>,</mo><mi>g</mi><mo>&apos;</mo><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dib</mi><mo>=</mo><mi>dibujar</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>,</mo><mi>q</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dib</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>r</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>rojo</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>sen</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><pi/><mo>*</mo><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac><mo>+</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r </correctAnswer><correctAnswer type="mathml"> #f </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Zuzenak lantzen Lau funtizo lineal ikusiko dituzu. Lotu behar dituzu adierazpen grafiko eta analitikoak.

]]> 1.0000000 0.3333333 0 true Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> #d1

]]> #sol1 #d2

]]> #sol2 #d3

]]> #sol3 #d4

]]> #sol4 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>x1</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>sol1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>x2</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t2</mi><mo>,</mo><mi>sol2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mo>(</mo><mi>x3</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t3</mi><mo>,</mo><mi>sol3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mo>(</mo><mi>x4</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t4</mi><mo>,</mo><mi>sol4</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zuzenaren ekuazioa identifikatu Begira ezazu irudi honetan azaltzen den zuzena. #fig2

Identifika ezazu hiru hauetatik zein den bere ekuazioa:

{#1}

]]> 1.0000000 0.3333333 0 Oso ongi, asmatu duzu!!!~%0%#r2#Ez duzu asmatu~%0%#r3#Ez duzu asmatu~%0%#r4#Ez duzu asmatu}]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>:=</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>:=</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>:=</mo><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>:=</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fig2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>r1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> GGZZ Matematika II Asintota bertikal bi eta horizontala Honako funtzioa kontuan hartuz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mi»i«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mi»i«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

Bere definizio eremua hau da: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfenced»«/math»

Asintota bertikaletako alboko limiteak kalkulatu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»d«/mi»«mo»-«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» = {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»d«/mi»«mo»+«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» = {#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»e«/mi»«mo»-«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» = {#3}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»e«/mi»«mo»+«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» = {#4}

Eta asintota horizontala dauka y = {#5} baliorako.

OHARRAK: Emaitza zatikia bada, zatiki bezala idatzi (adibidez 3/4)

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mi>poli1</mi><mi>poli2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdezk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mi>d</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdesk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mi>d</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeezk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mi>e</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeesk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mi>e</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dezkondo</mi><mo>=</mo><mi>limdezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dezktxarto</mi><mo>=</mo><mo>-</mo><mi>limdezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deskondo</mi><mo>=</mo><mi>limdesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desktxarto</mi><mo>=</mo><mo>-</mo><mi>limdesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eezkondo</mi><mo>=</mo><mi>limeezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eezktxarto</mi><mo>=</mo><mo>-</mo><mi>limeezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eeskondo</mi><mo>=</mo><mi>limeesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eesktxarto</mi><mo>=</mo><mo>-</mo><mi>limeesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>horizontala</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>funtzioa</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdezk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdesk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeezk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeesk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dezkondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dezktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deskondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eezkondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eezktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eeskondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eesktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>horizontala</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Asintota bertikala eta zehiarra Honako funtzioa kontuan hartuz: f(x) = #funtzioa

Asintota bertikaletako alboko limiteak kalkulatu:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»d«/mi»«mo»-«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math» = {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»L«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«msup»«mi»d«/mi»«mo»+«/mo»«/msup»«/mrow»«/munder»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math» = {#2}

Eta asintota zehiarraren ekuazioa honakoa da:

y = {#3}·x + {#4}

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mi>poli1</mi><mi>poli2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdezk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mi>d</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdesk</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mi>d</mi></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limezkondo</mi><mo>=</mo><mi>limdezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limezktxarto</mi><mo>=</mo><mo>-</mo><mi>limdezk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeskondo</mi><mo>=</mo><mi>limdesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limesktxarto</mi><mo>=</mo><mo>-</mo><mi>limdesk</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfrac><mi>funtzioa</mi><mi>x</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mo>(</mo><mi>funtzioa</mi><mo>-</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdezk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limdesk</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limezkondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limezktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limeskondo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limesktxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> Asintotak Zein asintota mota falta ?

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mn»1«/mn»«/math»

]]> #res1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mn»2«/mn»«/math»

]]> #res2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mn»3«/mn»«/math»

]]> #res3 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu1</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi></mrow><mrow><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res1</mi><mo>=</mo><mi>zehiarra</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b2</mi></mrow><mrow><mi>c2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res2</mi><mo>=</mo><mi>horizontala</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu3</mi><mo>=</mo><mfrac><mrow><mi>a3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b3</mi></mrow><mrow><mi>c3</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d3</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res3</mi><mo>=</mo><mi>bertikala</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zehiarra</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>horizontala</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bertikala</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Batez bestekoa eta desbideratze tipikoa «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»X«/mi»«mo»:«/mo»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»n«/mi»«mi»a«/mi»«mi»k«/mi»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»:«/mo»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»z«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mi»s«/mi»«mi»t«/mi»«mi»e«/mi»«mi»k«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»§#956;«/mi»«mo»=«/mo»«/math»

{#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»e«/mi»«mi»s«/mi»«mi»b«/mi»«mi»i«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»i«/mi»«mi»p«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»§#963;«/mi»«mo»=«/mo»«/math»

{#2}

]]> 1.0000000 0.1000000 0 true #g1

]]> #f1 #g2

]]> #f2 #g3

]]> #f3 #g4

]]> #f4 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msqrt><mi>x</mi></msqrt><mo>,</mo><msup><mn>2</mn><mi>x</mi></msup><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>funtzioa</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>s2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>s3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>s4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mo>-</mo><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>k</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>k</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>k</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>+</mo><mi>k</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>k</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g4</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mi>f4</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Jarraitasuna «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnspacing=¨1.4ex¨ columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mn»1«/mn»«/mtd»«mtd»«mi»x«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mn»2«/mn»«/mtd»«mtd»«mo»#«/mo»«mi»a«/mi»«mo»§lt;«/mo»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mi»j«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mi»i«/mi»«mi»t«/mi»«mi»u«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»a«/mi»«mo»§#160;«/mo»«/math»

]]> 1.0000000 1.0000000 0 Verdadero #p

]]> Falso #p

]]> 1.0000000 0.0000000 0 editor 15 0 <question/> limitea infinitura Kalkulatu ondoko limitea:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi mathvariant=¨normal¨»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mfrac»«mi»#poli1«/mi»«mi»#poli2«/mi»«/mfrac»«/math» = {#1}

OHARRA: Emaitza zatikia bada, zatiki bezala idatzi (adibidez 3/4). Infinitu bada, infinitu idatzi eta minus infinitu bada, -infinitu .

]]> 1.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi><mo>=</mo><mi>e</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>f</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mi>poli1</mi><mi>poli2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>emaitza</mi><mo>=</mo><cn>+∞</cn></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mi>infinitu</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>emaitza</mi><mo>=</mo><cn>-∞</cn></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mo>-</mo><mi>infinitu</mi></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mi>emaitza</mi></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>azkenemaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> limitea minus infinitura Kalkulatu ondoko limitea:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi mathvariant=¨normal¨»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mfrac»«mi»#poli1«/mi»«mi»#poli2«/mi»«/mfrac»«/math» = {#1}

OHARRA: Emaitza zatikia bada, zatiki bezala idatzi (adibidez 3/4). Infinitu bada, infinitu idatzi eta minus infinitu bada, -infinitu .

]]> 1.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi><mo>=</mo><mi>e</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>f</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mi>poli1</mi><mi>poli2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>-∞</cn></mrow></munder><mi>funtzioa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>emaitza</mi><mo>=</mo><cn>+∞</cn></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mi>infinitu</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>emaitza</mi><mo>=</mo><cn>-∞</cn></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mo>-</mo><mi>infinitu</mi></mrow><mrow><mi>azkenemaitza</mi><mo>=</mo><mi>emaitza</mi></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>azkenemaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>infinitu</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> limitea puntu batera Kalkulatu ondoko limitea:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mi»#a«/mi»«/mrow»«/munder»«mfrac»«mi»#poli1«/mi»«mi»#poli2«/mi»«/mfrac»«/math» = {#1}

]]> 1.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mi>poli1</mi><mi>poli2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mi>a</mi></mrow></munder><mi>funtzioa</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poli2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Matrizeak - batuketak - biderketak Bitez «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mi»#A«/mi»«/math» eta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mi»#B«/mi»«/math» matrizeak. Aukeratu erantzun egokiak:

]]> 1.0000000 1.0000000 0 false true abc A · B biderketa ezin da egin, biak dimentsio berekoak izan behar baitira

]]> A + B batuketa ezin da egin

]]> A · B kalkula dezakegu eta emaitza izango den matrizearen dimentsioa #b x #b da

]]> A · B kalkula dezakegu eta emaitza izango den matrizearen dimentsioa #a x #a

(emaitz bat baino gehiago posible dira)

]]> 1.0000000 1.0000000 0 false true abc Ezin dugu kalkulatu A · B

]]> Ezin dugu kalkulatu A + B

]]> A-ren irauliaren eta B-ren arteko biderketa egin dezakegu.

]]> A-ren alderantzizkoa kalkula dezakegu.

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #d

]]> #sol3

]]> #d

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mo>(</mo><msqrt><mrow><mo>(</mo><mi>b</mi><mo>-</mo><mi>B</mi><mo>)</mo><mo>^</mo><mn>2</mn><mo>-</mo><mn>4</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>A</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>c</mi><mo>-</mo><mi>C</mi><mo>)</mo></mrow></msqrt><mo>∉</mo><naturalnumbers/><mo>)</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd/></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>*</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>A1</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>A</mi><mo>≠</mo><mn>0</mn><mo> 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>región</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>par1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>par2</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo> </mo><mo>(</mo><mi>par1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>par2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>.</mo><mn>1</mn><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>.</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> prob - abc makinak - akstunak Lantegi batek torlojuak egiten dituzten hiru makina ditu. A makinak guztira egiten diren torlojuen % #a egiten ditu; B makinak, % #b, eta C makinak, % #c. Bestetik, A makinatik ateratzen diren torlojuetatik % #atxarto akastunak dira; B-tik % #btxarto eta C-tik % #ctxarto.

(OHARRA: Emaitza zatiki eran ipini, adibidez 4/15; sinplifikatu beharrik ez dago)

a)Lantegi horretatik atera den torloju bat akastuna izateko probabilitatea kalkulatu: {#1}

b)Ze probabilitate dago akastuna izan den torloju bat A makinakoa izateko: {#2}

]]> 2.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atxarto</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>btxarto</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ctxarto</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PA</mi><mo>=</mo><mfrac><mi>a</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PB</mi><mo>=</mo><mfrac><mi>b</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PC</mi><mo>=</mo><mfrac><mi>c</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PAtxarto</mi><mo>=</mo><mfrac><mi>atxarto</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PBtxarto</mi><mo>=</mo><mfrac><mi>btxarto</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PCtxarto</mi><mo>=</mo><mfrac><mi>ctxarto</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pakastuna</mi><mo>=</mo><mi>PA</mi><mo>*</mo><mi>PAtxarto</mi><mo>+</mo><mi>PB</mi><mo>*</mo><mi>PBtxarto</mi><mo>+</mo><mi>PC</mi><mo>*</mo><mi>PCtxarto</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pakoabaldinakastuna</mi><mo>=</mo><mfrac><mrow><mi>PA</mi><mo>*</mo><mi>PAtxarto</mi></mrow><mi>pakastuna</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>btxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ctxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PB</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PAtxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>100</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PBtxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>50</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PCtxarto</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>100</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pakastuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>23</mn><mn>500</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pakoabaldinakastuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>15</mn><mn>46</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> prob - kutxa bi - batetik bestera bola pasa Demagun bi kutxa ditugula, A eta B. A kutxan #B1 bola beltz eta #G1 bola gorri daude. B kutxan, ordea, #B2 bola beltz, #G2 bola gorri eta #U2 bola urdin daude. A kutxatik bola bat atera eta B kutxan sartu ondoren, B kutxa honetatik beste bola bat ateratzen badugu, kalkulatu ondoko probabilitate hauek:

(OHARRA: Emaitza zatiki eran ipini, adibidez 4/15; sinplifikatu beharrik ez dago)

a) Bi bolak gorriak izateko probabilitatea: {#1}

b) Bigarren bola gorria izateko probabilitatea: {#2}

c) Bigarren bola urdina izateko probabilitatea: {#3}

d) Bigarren bola gorria atera bada, zein izango da 1. bola beltza izateko probabilitatea: {#4}

]]> 4.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mn>10</mn><mo>-</mo><mi>B1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U2</mi><mo>=</mo><mn>9</mn><mo>-</mo><mi>B2</mi><mo>-</mo><mi>G2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pbiakgorriak</mi><mo>=</mo><mfrac><mrow><mi>G1</mi><mo>*</mo><mo>(</mo><mi>G2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2gorria</mi><mo>=</mo><mfrac><mrow><mi>G1</mi><mo>*</mo><mo>(</mo><mi>G2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>100</mn></mfrac><mo>+</mo><mfrac><mrow><mi>B1</mi><mo>*</mo><mi>G2</mi></mrow><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2urdina</mi><mo>=</mo><mfrac><mi>U2</mi><mn>10</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pbaldintzatua</mi><mo>=</mo><mfrac><mfrac><mrow><mi>B1</mi><mo>*</mo><mi>G2</mi></mrow><mn>100</mn></mfrac><mi>p2gorria</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pbiakgorriak</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>10</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2gorria</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>25</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2urdina</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pbaldintzatua</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Probabilitatea binomialarekin II «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»u«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mi»g«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»o«/mi»«mi»b«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»l«/mi»«mi»i«/mi»«mi»t«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mo»:«/mo»«mspace linebreak=¨newline¨/»«mi»X«/mi»«mo»=«/mo»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»p«/mi»«mo»(«/mo»«mi»X«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»E«/mi»«mi»r«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»l«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»i«/mi»«mi»f«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»m«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»a«/mi»«mi»r«/mi»«/math»

]]> 3.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo> </mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>a</mi><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mi>i</mi></apply><mo>*</mo><msup><mi>p</mi><mi>i</mi></msup><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>p</mi><msup><mo>)</mo><mrow><mi>n</mi><mo>-</mo><mi>i</mi></mrow></msup></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mrow><mi>i</mi><mo>=</mo><mi>k</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precisión</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.8875</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Probabilitateak binomialarrekin «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»u«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mi»g«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»o«/mi»«mi»b«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»l«/mi»«mi»i«/mi»«mi»t«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mspace linebreak=¨newline¨/»«mi»X«/mi»«mo»=«/mo»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»p«/mi»«mo»(«/mo»«mi»X«/mi»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»§#160;«/mo»«mi»E«/mi»«mi»r«/mi»«mi»a«/mi»«mi»b«/mi»«mi»i«/mi»«mi»l«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»i«/mi»«mi»f«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»m«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»a«/mi»«mi»r«/mi»«mo»)«/mo»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo> </mo><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mi>k</mi></apply><mo>*</mo><msup><mi>p</mi><mi>k</mi></msup><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>p</mi><msup><mo>)</mo><mrow><mi>n</mi><mo>-</mo><mi>k</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precisión</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.2855</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Programazio lineala - buruketa Lantegi batean jakak eta prakak egiten dituzte. Horiek egiteko bi makina erabiltzen dira (ebakitzekoa eta jostekoa).

Jaka bat egiteko ebakitzeko makina #kxa minutu erabili behar da eta jostekoa #kxb.

Praka bat egiteko ebakitzeko makina #kya minutu erabili behar da eta jostekoa #kyb.

Ebakitzeko makina #ikurra1 #ka minutu erabili behar da eta jostekoa #ikurra2 #kb minutu.

Egindako guztia saldu egiten dute, eta irabaziak hauek dira: #xf euro jaka bakoitzeko eta #yf euro praka bakoitzeko.

Zenbat jaka eta zenbat praka egin beharko dira irabazia maximoa izateko?

Emaitza izango den puntua:

x = {#1}

y = {#2}

Eta lortutako balio maximoa: {#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ya</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mfrac><mrow><mi>xo</mi><mo>*</mo><mi>ya</mi></mrow><mrow><mi>ya</mi><mo>-</mo><mi>yo</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mfrac><mrow><mi>xo</mi><mo>*</mo><mi>yb</mi></mrow><mrow><mi>yb</mi><mo>-</mo><mi>yo</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ainekuazioaezezaguna</mi><mo>=</mo><mi>ya</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>xa</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ainekuazioazenbakia</mi><mo>=</mo><mi>xa</mi><mo>*</mo><mi>ya</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>binekuazioaezezaguna</mi><mo>=</mo><mi>yb</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>xb</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>binekuazioazenbakia</mi><mo>=</mo><mi>xb</mi><mo>*</mo><mi>yb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kxa</mi><mo>=</mo><mi>ya</mi><mo>*</mo><mo>(</mo><mi>ya</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kya</mi><mo>=</mo><mi>xa</mi><mo>*</mo><mo>(</mo><mi>ya</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kxb</mi><mo>=</mo><mi>yb</mi><mo>*</mo><mo>(</mo><mi>yb</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kyb</mi><mo>=</mo><mi>xb</mi><mo>*</mo><mo>(</mo><mi>yb</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ka</mi><mo>=</mo><mi>ainekuazioazenbakia</mi><mo>*</mo><mo>(</mo><mi>ya</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kb</mi><mo>=</mo><mi>binekuazioazenbakia</mi><mo>*</mo><mo>(</mo><mi>yb</mi><mo>-</mo><mi>yo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mi>A</mi></mrow><mtable><mtr><mtd><mi>ikurra1</mi><mo>=</mo><mi>gehienez</mi></mtd></mtr><mtr><mtd><mi>ikurra2</mi><mo>=</mo><mi>gehienez</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>yb</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>yb</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>xa</mi><mo>*</mo><mi>xf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>yb</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xa</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>xa</mi><mo>*</mo><mi>xf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xo</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>yo</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xa</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mi>B</mi></mrow><mtable><mtr><mtd><mi>ikurra1</mi><mo>=</mo><mi>gehienez</mi></mtd></mtr><mtr><mtd><mi>ikurra2</mi><mo>=</mo><mi>gutxienez</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>yb</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>yb</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>ya</mi><mo>*</mo><mi>yf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>yb</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>ya</mi></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>ya</mi><mo>*</mo><mi>yf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xo</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>yo</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>ya</mi></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mi>C</mi></mrow><mtable><mtr><mtd><mi>ikurra1</mi><mo>=</mo><mi>gutxienez</mi></mtd></mtr><mtr><mtd><mi>ikurra2</mi><mo>=</mo><mi>gehienez</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xa</mi><mo>*</mo><mi>xf</mi><mo>></mo><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xa</mi><mo>*</mo><mi>xf</mi><mo>></mo><mi>xb</mi><mo>*</mo><mi>xf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xa</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xb</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xo</mi><mo>*</mo><mi>xf</mi><mo>+</mo><mi>yo</mi><mo>*</mo><mi>yf</mi><mo>></mo><mi>xb</mi><mo>*</mo><mi>xf</mi></mrow><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xo</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>yo</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>xb</mi></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></apply></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>femaitza</mi><mo>=</mo><mi>xf</mi><mo>*</mo><mi>xemaitza</mi><mo>+</mo><mi>yf</mi><mo>*</mo><mi>yemaitza</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ainekuazioaezezaguna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>7</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ainekuazioazenbakia</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>98</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>binekuazioaezezaguna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>binekuazioazenbakia</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>49</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ya</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kxa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kya</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kxb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kyb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ka</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>196</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xemaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yemaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>femaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Sistemak matrizeekin Ebatzi hurrengo sistema. X eta Y matrizeak dira.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨¨ close=¨}¨»«mtable columnalign=¨right¨»«mtr»«mtd»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»X«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»k«/mi»«mn»2«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mi»Y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»k«/mi»«mn»3«/mn»«mo»§#183;«/mo»«mi»X«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»k«/mi»«mn»4«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mi»Y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»B«/mi»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Idatzi soluzioa

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»X«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd/»«mtd/»«/mtr»«mtr»«mtd/»«mtd/»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mi»Y«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd/»«mtd/»«/mtr»«mtr»«mtd/»«mtd/»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.2000000 0 0 X=#XsolY=#Ysol]]> Ondo

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mo>(</mo><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>absoluto</mi><mo>(</mo><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi><mo>)</mo><mo><</mo><mn>10</mn><mo>)</mo><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd><mtd><mi>aleatorio</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Xsol</mi><mo>=</mo><mfenced><mfrac><mn>1</mn><mrow><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi></mrow></mfrac></mfenced><mo>*</mo><mfenced><mrow><mi>k4</mi><mo>*</mo><mi>B1</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>B2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ysol</mi><mo>=</mo><mfenced><mfrac><mn>1</mn><mrow><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi></mrow></mfrac></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mi>k3</mi><mo>*</mo><mi>B1</mi><mo>+</mo><mi>k1</mi><mo>*</mo><mi>B2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Xsol</mi><mo>=</mo><mfenced><mfrac><mn>1</mn><mrow><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi></mrow></mfrac></mfenced><mo>*</mo><mfenced><mrow><mi>k4</mi><mo>*</mo><mi>B1</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>B2</mi></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></mtd><mtd><mfrac><mn>6</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ysol</mi><mo>=</mo><mfenced><mfrac><mn>1</mn><mrow><mi>k1</mi><mo>*</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>k3</mi></mrow></mfrac></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mi>k3</mi><mo>*</mo><mi>B1</mi><mo>+</mo><mi>k1</mi><mo>*</mo><mi>B2</mi></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mn>6</mn><mn>7</mn></mfrac></mtd><mtd><mfrac><mn>3</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mo>#</mo><mi>X</mi><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>Y</mi><mo>=</mo><mo>#</mo><mi>Y</mi><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Triangeluak «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mi»m«/mi»«mi»e«/mi»«mi»t«/mi»«mi»r«/mi»«mi»o«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»A«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»C«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»r«/mi»«mi»p«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mi»k«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»e«/mi»«mi»l«/mi»«mi»u«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»z«/mi»«mi»a«/mi»«mi»l«/mi»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mo»#«/mo»«mi»a«/mi»«mi»z«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»z«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»k«/mi»«mi»o«/mi»«/math»

{#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mi»a«/mi»«mi»l«/mi»«mi»i«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mi»k«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»k«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»A«/mi»«mi»B«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»A«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»s«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»u«/mi»«mi»t«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»e«/mi»«mi»l«/mi»«mi»u«/mi»«mi»a«/mi»«mo»(«/mo»«mo»§#160;«/mo»«mi»r«/mi»«mi»a«/mi»«mi»d«/mi»«mi»i«/mi»«mi»a«/mi»«mi»n«/mi»«mi»e«/mi»«mi»tan«/mi»«mo»)«/mo»«/math»

{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>estado_geometría</mi><mfenced><mtext>"2D"</mtext></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ale</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>:</mo><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>ale</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>ale</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>:</mo><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>ale</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>ale</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>:</mo><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>ale</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>ale</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>c1</mi><mo>.</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mo>:</mo><mo>=</mo><mi>triángulo</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>aza</mi><mo>:</mo><mo>=</mo><mi>área</mi><mo>(</mo><mi>t</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>aza</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>c1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL2</mi><mo>=</mo><mi>ángulo</mi><mo>(</mo><mi>t</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL3</mi><mo>=</mo><mi>ángulo</mi><mo>(</mo><mi>t</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL4</mi><mo>=</mo><mi>ángulo</mi><mo>(</mo><mi>t</mi><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.46365</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zatiketaren deribatua Zein da honako funtzioaren deribatua?

f(x) = #funtzioa

]]> 1.0000000 1.0000000 0 true true none #deribatua #funtzio1 #funtzio2 #funtzio3 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mi>sen</mi><mo>(</mo><mi>x</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mfrac><mn>1</mn><mi>x</mi></mfrac></mfrac></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mo>(</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo><mo>*</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow><mrow><mo>(</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><exponentiale/><mi>x</mi></msup></mfrac></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><msup><exponentiale/><mi>x</mi></msup></mfrac></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><msup><exponentiale/><mrow><mn>2</mn><mi>x</mi></mrow></msup></mfrac></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo><mo>*</mo><msup><exponentiale/><mi>x</mi></msup><mo>+</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><msup><exponentiale/><mi>x</mi></msup></mrow><msup><exponentiale/><mrow><mn>2</mn><mi>x</mi></mrow></msup></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo><mo>*</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mi>h</mi><mo>(</mo><mi>x</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo><mo>*</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>'</mo></mrow><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deribatua</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> Matematika I 1Funtzio Hiperbolikoak: Asintotak eta Adierazpen Grafikoa f(x) = #p funtzioa izanik, esan esazu bere asintotak zeintzuk diren

Asintota Bertikala: x = {#1}

Asintota Horizontala: y = {#2}

Eta identifikatu bere grafikoa zein den

{#3}

Asintota Bertikala: x = {#1}

Asintota Horizontala: y = {#2}

eta identifikatu bere grafikoa zein den

{#3}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»sin«/mi»«mi»t«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»B«/mi»«mi»e«/mi»«mi»r«/mi»«mi»t«/mi»«mi»i«/mi»«mi»k«/mi»«mi»a«/mi»«mi»l«/mi»«mi»a«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«/math» {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»sin«/mi»«mi»t«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»H«/mi»«mi»o«/mi»«mi»r«/mi»«mi»i«/mi»«mi»z«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mi»a«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»=«/mo»«/math» {#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»f«/mi»«mi»i«/mi»«mi»k«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»r«/mi»«mi»a«/mi»«mi»f«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»e«/mi»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mspace linebreak=¨newline¨/»«/math»

{#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow/></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow/></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tablero</mi><mfenced><mrow/></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>:=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>·</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>:=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>k</mi></mrow><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfrac><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>#</mo><mn>3</mn><mo>"</mo><mo>,</mo><mi>k</mi><mo>,</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>#</mo><mn>3</mn><mo>"</mo><mo>,</mo><mi>k</mi><mo>,</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>==</mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>"</mo><mo>,</mo><mi>k</mi><mo>,</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>representar</mi><mfenced><mrow><mi>s1</mi><mo>,</mo><mi>p</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>representar</mi><mfenced><mrow><mi>s2</mi><mo>,</mo><mi>m</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>representar</mi><mfenced><mrow><mi>s3</mi><mo>,</mo><mi>n</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">true</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4 Funtzio Hiperbolikoak: Asintotak eta Adierazpen Grafikoa.eta Grafikoa. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»n«/mi»«mi»i«/mi»«mi»k«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»s«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»e«/mi»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»u«/mi»«mi»k«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»i«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»sin«/mi»«mi»t«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mi»k«/mi»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»f«/mi»«mi»i«/mi»«mi»k«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mi»e«/mi»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»d«/mi»«mi»i«/mi»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mi»z«/mi»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»r«/mi»«mi»a«/mi»«mi»f«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

{#3}

k = +/-{#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math» eta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

k = {#1}

]]> 1.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><mfrac><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi></mrow><mi>v1</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Biderketa baten deribatua. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»b«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mi»a«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»O«/mi»«mi»h«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mo»:«/mo»«mspace linebreak=¨newline¨/»«mi»E«/mi»«mi»r«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»u«/mi»«mi»n«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mo»`«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mo»§#160;«/mo»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»t«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»e«/mi»«mi»r«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»b«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mi»a«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»A«/mi»«mi»d«/mi»«mi»i«/mi»«mi»b«/mi»«mi»i«/mi»«mi»d«/mi»«mi»e«/mi»«mi»z«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mo»`«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.2000000 0 0 #d]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak_1</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>·</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>f</mi><mo>=</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mi>n</mi></msup><mo>,</mo><msup><exponentiale/><mi>x</mi></msup><mo>,</mo><mi>sin</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>cos</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>tan</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>ln</mi><mfenced><mi>x</mi></mfenced></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mi>n</mi></msup><mo>,</mo><msup><exponentiale/><mi>x</mi></msup><mo>,</mo><mi>sin</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>cos</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>tan</mi><mfenced><mi>x</mi></mfenced><mo>,</mo><mi>ln</mi><mfenced><mi>x</mi></mfenced></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mi>f</mi><mo>≠</mo><mi>g</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>f</mi><mo>·</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>deribatua</mi><mfenced><mi>p</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>sin</mi><mfenced><mi>x</mi></mfenced><mo>*</mo><mi>ln</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>5</mn><mo>*</mo><mi>sin</mi><mfenced><mi>x</mi></mfenced></mrow><mi>x</mi></mfrac><mo>-</mo><mn>5</mn><mo>*</mo><mi>ln</mi><mfenced><mi>x</mi></mfenced><mo>*</mo><mi>cos</mi><mfenced><mi>x</mi></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">d</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Deribatuak: berreketak eta erroak f(x) = #p funtzioaren funtzio deribatua ondoko hau da:

f '(x) = {#1}

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mi>n</mi></msup><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mi>n</mi></msup></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><msup><mi>x</mi><mi>m</mi></msup></msqrt><mo>,</mo><mfrac><mn>1</mn><msqrt><msup><mi>x</mi><mi>m</mi></msup></msqrt></mfrac><mo>,</mo><mroot><msup><mi>x</mi><mi>m</mi></msup><mi>r</mi></mroot><mo>,</mo><mfrac><mn>1</mn><mroot><msup><mi>x</mi><mi>m</mi></msup><mi>r</mi></mroot></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>f</mi><mo>·</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>derivar</mi><mfenced><mi>p</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><msup><mi>x</mi><mn>3</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/><data name="cas">add</data></localData></question> Deribatuak: Erroak eta polinomioak

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»b«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mi»a«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»O«/mi»«mi»h«/mi»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mi»E«/mi»«mi»r«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»u«/mi»«mi»n«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mi»h«/mi»«mi»a«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»u«/mi»«mi»z«/mi»«mi»u«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»`«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»x«/mi»«mroot»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/mrow»«mn»5«/mn»«/mroot»«/mrow»«mrow»«mn»5«/mn»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»i«/mi»«mi»t«/mi»«mi»z«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mi»i«/mi»«mi»z«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mi»t«/mi»«mi»a«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.2000000 0 0 f'(x)=#s]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mroot><mrow><mi>a</mi><mo>·</mo><msup><mi>x</mi><mi>m</mi></msup><mo>+</mo><mi>b</mi><mo>·</mo><msup><mi>x</mi><mrow><mi>m</mi><mo>-</mo><mn>2</mn></mrow></msup></mrow><mi>n</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>derivar</mi><mfenced><mi>p</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></mrow><mn>4</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mroot><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></mrow><mn>4</mn></mroot></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">true</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Laburtu, arrazionalizatu, ...

]]> Ekuazio sistemaren ebazpena - GAUSS Ebatzi ondoko ekuazio sistema:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#c1«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b2«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#c2«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a3«/mi»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b3«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#c3«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

x={#1}

y={#2}

z={#3}

]]> 1.0000000 0.2000000 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #g1

]]> #f1 #g2

]]> #f2 #g3

]]> #f3 #f4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak_1</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>*</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>*</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>k</mi></mrow><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mo>-</mo><mi>k</mi></mrow><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><msub><mfenced><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mo>-</mo><mi>k</mi></mrow><mrow><mi>x</mi><mo>+</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f3</mi></mtd></mtr></mtable></mfenced></mrow></mfenced><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>adierazi</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>adierazi</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g3</mi><mo>=</mo><mi>adierazi</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzioak eta grafikoak Aukeratu zein den f(x)=#h funtzioaren adierazpen grafiko egokia.

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #graf1

]]> #graf2

]]> #graf3

]]> #graf4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>s1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>anchura_ventana</mi><mo>=</mo><mn>260</mn><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>anchura_ventana</mi><mo>=</mo><mn>260</mn><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>anchura_ventana</mi><mo>=</mo><mn>260</mn><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>s4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>anchura_ventana</mi><mo>=</mo><mn>260</mn><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>x_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>·</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>·</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>a</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>·</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>s1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf2</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>s2</mi><mo>,</mo><mo>-</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf3</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>s3</mi><mo>,</mo><mi>f</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf4</mi><mo>=</mo><mi>dibujar</mi><mfenced><mrow><mi>s4</mi><mo>,</mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mn>1</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/><data name="cas">add</data></localData></question> Funtzioak: adierazpen analitiko eta grafikoa. f(x)=#h funtzioa eta ondoko funtzioa bat datoz?

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow/></mfenced><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>f</mi><mfenced><mrow/></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mfenced><mrow/></mfenced><mo>,</mo><mi>g</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>dibujar</mi><mfenced><mi>g</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mfenced><mrow><mi>g</mi><mo>=</mo><mi>h</mi></mrow></mfenced><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Funtzioen grafikoak aldakuntzak eginez (EGIA/GEZURRA) Honako grafikoan gorriz ikus dezakezu f(x) = #f3 funtzioa. Aldakuntza egokiak egin ondoren, urdinez marraztutakoa f(x) = #h funtzioarena al da?

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mn>2</mn><mi>x</mi></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msup><mi>x</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mo>)</mo><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo>-</mo><mi>f1</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo><mo>+</mo><mn>2</mn><mo>,</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>f1</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>g</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>f2</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>f1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>f2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mi>f2</mi><mo>=</mo><mi>h</mi><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mi>f2</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi><mo>,</mo><msqrt><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msqrt><mo>+</mo><mn>2</mn><mo>,</mo><mo>-</mo><msqrt><mrow><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><mn>2</mn><mo>,</mo><mi>falso</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> Geometria-CLOZE AB segmentuaren puntu erdiaren koordenatuak M(#m1,#m2) badira, kalkula ezazu B puntuaren koordenatuak, A puntuarenak (#a1,#a2) direla jakinik.

{#1}

Zelan deitzen da Mtik pasatzen den AB segmentuarekiko perpendikularra den zuzena? {#2}

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>:=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mn>2</mn><mo>·</mo><mi>m1</mi><mo>+</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mn>2</mn><mo>·</mo><mi>m2</mi><mo>+</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>m2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>:</mo><mo>=</mo><mi>B</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Hiru ezezaguneko eta hiru ekuazioko sistemen ebazpena Gauss-en metodoaz Ebatzi ondorengo sistema Gauss-en metodoaz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mrow»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c1«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c2«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a3«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b3«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c3«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«mo»§nbsp;«/mo»«/mrow»«/mfenced»«/math»

OHARRA: Eman erantzuna adierazten den ordena eta formatua erabiliz:

x=
y=
z=

Sistema Bateragarri eta Indeterminatua bada, aukera ezazu z aldagaitzat eta idatzi z = k eta y eta z

k-ren funtziopean (gogoratu koefizientea eta letraren arteko biderketa · ikurraren bidez adierazi behar duzula)

]]> 1.0000000 0.1000000 0 0 x=#xy=#yz=#z]]> Muy bien. Se trata de un sistema compatible determinado y estaes su única solución.

]]> <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>a</mi><mn>1</mn></msub></mtd><mtd><msub><mi>b</mi><mn>1</mn></msub></mtd><mtd><msub><mi>c</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>2</mn></msub></mtd><mtd><msub><mi>b</mi><mn>2</mn></msub></mtd><mtd><msub><mi>c</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>3</mn></msub></mtd><mtd><msub><mi>b</mi><mn>3</mn></msub></mtd><mtd><msub><mi>c</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mrow><mi>d</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>d</mi><mo>,</mo><msub><mi>a</mi><mi>i</mi></msub><mo>·</mo><mi>x</mi><mo>+</mo><msub><mi>b</mi><mi>i</mi></msub><mo>·</mo><mi>y</mi><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>·</mo><mi>z</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>a</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msub><mi>a</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>b</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>b</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>b</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>c</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>c</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msub><mi>c</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msub><mi>d</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msub><mi>d</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><msub><mi>d</mi><mn>3</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mi>#z</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> Hiru ezezaguneko eta hiru ekuazioko sistemen ebazpena Gauss-en metodoaz Ebatzi ondorengo sistema Gauss-en metodoaz:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mrow»«mtable»«mtr»«mtd»«mi»#a1«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b1«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c1«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a2«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b2«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c2«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a3«/mi»«mo»·«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#b3«/mi»«mo»·«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mi»#c3«/mi»«mo»·«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«mo»§nbsp;«/mo»«/mrow»«/mfenced»«/math»

OHARRA: Eman erantzuna adierazten den ordena eta formatua erabiliz:

x=
y=
z=

Sistema Bateragarri eta Indeterminatua bada, aukera ezazu z aldagaitzat eta idatzi z = k eta y eta z

k-ren funtziopean (gogoratu koefizientea eta letraren arteko biderketa · ikurraren bidez adierazi behar duzula)

]]> 1.0000000 0.1000000 0 0 x=#xy=#yz=#z]]> Muy bien. Se trata de un sistema compatible determinado y estaes su única solución.

]]> <question><wirisCasSession><session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>a</mi><mn>1</mn></msub></mtd><mtd><msub><mi>b</mi><mn>1</mn></msub></mtd><mtd><msub><mi>c</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>2</mn></msub></mtd><mtd><msub><mi>b</mi><mn>2</mn></msub></mtd><mtd><msub><mi>c</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>3</mn></msub></mtd><mtd><msub><mi>b</mi><mn>3</mn></msub></mtd><mtd><msub><mi>c</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mi>A</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mi>L</mi></mrow><mrow><mi>d</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>d</mi><mo>,</mo><msub><mi>a</mi><mi>i</mi></msub><mo>·</mo><mi>x</mi><mo>+</mo><msub><mi>b</mi><mi>i</mi></msub><mo>·</mo><mi>y</mi><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>·</mo><mi>z</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msub><mi>a</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msub><mi>a</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msub><mi>b</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msub><mi>b</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msub><mi>b</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>c</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>c</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msub><mi>c</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msub><mi>d</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msub><mi>d</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><msub><mi>d</mi><mn>3</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>#x</mi><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mi>#y</mi><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mi>#z</mi></math></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="cas">false</data></localData></question> Hirugarren mailako ekuazioa Ebatzi ondorengo ekuazioa #ecu =0, idatzi soluzioak txikienetik handienera ordenatuta.
x₁={#1}
x₂={#2}
x₃={#3}

]]> 3.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>x1</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>coc</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>+</mo><mi>res</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>31</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>62</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>35</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Hirugarren mailako ekuazioa Ebatzi ondorengo ekuazioa #ecu =0, idatzi soluzioak txikienetik handienera ordenatuta.
x₁={#1}
x₂={#2}
x₃={#3}

]]> 3.0000000 0.1000000 0 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>x1</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>coc</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>+</mo><mi>res</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>31</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>62</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>35</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Polinomio baten deribatua kalkulatu f(x) = #p funtzioaren deribatua.

Oharra:

Emaitza ondo izateko f'(x) = idatzi behar duzue eta gero deribatua.

Adibidez «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 f'x=#s]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mi style="color:#ffc800">aldagaiak_1</mi><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>·</mo><mi>ausazko</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>·</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>·</mo><msup><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>·</mo><msup><mi>x</mi><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>deribatua</mi><mfenced><mi>p</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session> ]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">true</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Polinomio baten faktorizazioa Faktorizatu honako poloinomioa: P(x) = #polinomioa

]]> 1.0000000 0.1000000 0 0 #emaitza]]> Oso ondo!

]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>polinomioa</mi><mo>=</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><mi>faktorizatu</mi><mo>(</mo><mi>polinomioa</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>polinomioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>m</mi><mi>a</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>z</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Puntu eta zuzen inplizituaren arteko distantzia (2D) Bilatu P=(#p1,#p2) puntutik r zuzenera dagoen distantzia.

r: (#a) x + (#b) y + (#c) = 0

Emaitza: Dist (P,r) = {#1}

]]> 1.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precisión</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dist</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>p1</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>p2</mi><mo>+</mo><mi>c</mi></mrow></mfenced><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>distantzia</mi><mo>=</mo><mi>a_decimal</mi><mo>(</mo><mi>dist</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dist</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>distantzia</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="precision">3</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zuzenaren ekuazioa - beste baten elkarzuta-paraleloa (2D) Bilatu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math» puntutik pasatzen den eta honako r zuzenaren #kokapena den zuzenaren ekuazio esplizitua:

#adierazpena

Datu hauek kontuan hartu: a1=#q1 , a2=#q2 , b1=#v1 , b2=#v2

Emaitza: y = {#1}·x + {#2}

]]> 2.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kokapena</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>paraleloa</mi><mo>,</mo><mi>elkarzuta</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zuzenmota</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>bektoriala</mi><mo>,</mo><mi>parametrikoa</mi><mo>,</mo><mi>jarraia</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>kokapena</mi><mo>=</mo><mi>paraleloa</mi></mrow><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>v2</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mo>-</mo><mi>v2</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>v1</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mi>b2</mi><mi>b1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>b2</mi><mo>*</mo><mi>p1</mi></mrow><mi>b1</mi></mfrac><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>zuzenmota</mi><mo>=</mo><mi>bektoriala</mi></mrow><mrow><mi>adierazpena</mi><mo>=</mo><mo>"</mo><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>+</mo><mi>t</mi><mo>*</mo><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>zuzenmota</mi><mo>=</mo><mi>parametrikoa</mi></mrow><mrow><mi>adierazpena</mi><mo>=</mo><mo>"</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>t</mi><mo>*</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>t</mi><mo>*</mo><mi>b2</mi></mtd></mtr></mtable></mfenced><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>zuzenmota</mi><mo>=</mo><mi>jarraia</mi></mrow><mrow><mi>adierazpena</mi><mo>=</mo><mo>"</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow><mi>b1</mi></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow><mi>b2</mi></mfrac><mo>"</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zuzenaren ekuazioa - inplizituaren elkarzuta/paraleloa Bilatu P=(#p1,#p2) puntutik pasatzen den eta honako r zuzenaren #kokapena den zuzenaren ekuazio esplizitua:

r: (#a) x + (#b) y + (#c) = 0

Emaitza: y = {#1}·x + {#2}

y = {#1}·x + {#2}

r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a1«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#b1«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#c1«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math»

s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a2«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#b2«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#c2«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math»

Esan zein den beraien arteko posizio erlatiboa:

]]> 1.0000000 1.0000000 0 true true abc #aerantzuna #berantzuna #cerantzuna #derantzuna <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>paraleloak</mi><mo>,</mo><mi>koinzidenteak</mi><mo>,</mo><mi>ebakitzaileak</mi><mo>,</mo><mi>elkarzutak</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>paraleloak</mi></mrow><mtable><mtr><mtd><mi>b2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><mi>b1</mi></mrow><mi>a1</mi></mfrac></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><mi>c1</mi></mrow><mi>a1</mi></mfrac><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>koinzidenteak</mi></mrow><mtable><mtr><mtd><mi>b2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><mi>b1</mi></mrow><mi>a1</mi></mfrac></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><mi>c1</mi></mrow><mi>a1</mi></mfrac></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>ebakitzaileak</mi></mrow><mtable><mtr><mtd><mi>b2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>*</mo><mi>b1</mi></mrow><mi>a1</mi></mfrac><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>elkarzutak</mi></mrow><mtable><mtr><mtd><mi>b2</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>a2</mi></mrow><mi>b1</mi></mfrac></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>koinzidenteak</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Koinzidenteak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>berantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Paraleloak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ebaki</ms><mo> </mo><ms>egiten</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>derantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Elkarzutak</ms><mo> </mo><ms>dira</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Zuzenen arteko posizio erlatiboa (inplizitua - jarraia) (2D) Honako zuzenen ekuazioak kontuan hartuz:

r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#c«/mi»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math»

s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»#p1«/mi»«/mrow»«mrow»«mi»#d1«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»#p2«/mi»«/mrow»«mrow»«mi»#d2«/mi»«/mrow»«/mfrac»«/math»

Esan zein den beraien arteko posizio erlatiboa:

]]> 1.0000000 1.0000000 0 true true abc #aerantzuna #berantzuna #cerantzuna #derantzuna <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>paraleloak</mi><mo>,</mo><mi>koinzidenteak</mi><mo>,</mo><mi>ebakitzaileak</mi><mo>,</mo><mi>elkarzutak</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>paraleloak</mi></mrow><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>d1</mi></mrow><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>d1</mi><mo>*</mo><mi>p2</mi><mo>-</mo><mi>d2</mi><mo>*</mo><mi>p1</mi><mo>)</mo></mrow><mi>d2</mi></mfrac><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>koinzidenteak</mi></mrow><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>d1</mi></mrow><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>d1</mi><mo>*</mo><mi>p2</mi><mo>-</mo><mi>d2</mi><mo>*</mo><mi>p1</mi><mo>)</mo></mrow><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>ebakitzaileak</mi></mrow><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>d1</mi></mrow><mi>d2</mi></mfrac><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>d1</mi><mo>*</mo><mi>p2</mi><mo>-</mo><mi>d2</mi><mo>*</mo><mi>p1</mi><mo>)</mo></mrow><mi>d2</mi></mfrac><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>elkarzutak</mi></mrow><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraleloak</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Paraleloak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>berantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Koinzidenteak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ebaki</ms><mo> </mo><ms>egiten</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>derantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Elkarzutak</ms><mo> </mo><ms>dira</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Zuzenen arteko posizio erlatiboa (jarraia - parametrikoa) (2D) Honako zuzenen ekuazioak kontuan hartuz:

r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»(«/mo»«mi»#p1«/mi»«mo»)«/mo»«/mrow»«mi»#d1«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»(«/mo»«mi»#p2«/mi»«mo»)«/mo»«/mrow»«mi»#d2«/mi»«/mfrac»«/math»

s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»#q1«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mi»t«/mi»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#v1«/mi»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»#q2«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mi»t«/mi»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»#v2«/mi»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Esan zein den beraien arteko posizio erlatiboa:

]]> 1.0000000 1.0000000 0 true true abc #aerantzuna #berantzuna #cerantzuna #derantzuna <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mi>paraleloak</mi><mo>,</mo><mi>koinzidenteak</mi><mo>,</mo><mi>ebakitzaileak</mi><mo>,</mo><mi>elkarzutak</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>paraleloak</mi></mrow><mtable><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mfrac><mrow><mi>v1</mi><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>q1</mi><mo>-</mo><mi>p1</mi><mo>)</mo><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac><mo>+</mo><mi>p2</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>koinzidenteak</mi></mrow><mtable><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mfrac><mrow><mi>v1</mi><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>q1</mi><mo>-</mo><mi>p1</mi><mo>)</mo><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac><mo>+</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>ebakitzaileak</mi></mrow><mtable><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mfrac><mrow><mi>v1</mi><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>q1</mi><mo>-</mo><mi>p1</mi><mo>)</mo><mo>*</mo><mi>d2</mi></mrow><mi>d1</mi></mfrac><mo>+</mo><mi>p2</mi><mo>+</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resultado</mi><mo>=</mo><mi>elkarzutak</mi></mrow><mtable><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>v1</mi><mo>*</mo><mi>d1</mi></mrow><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd><mi>q2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Elkarzutak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>berantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Koinzidenteak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cerantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Ebaki</mi><mo> </mo><mi>egiten</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>derantzuna</mi><mo>=</mo><mo>&quot;</mo><mi>Paraleloak</mi><mo> </mo><mi>dira</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>elkarzutak</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Elkarzutak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>berantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Koinzidenteak</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cerantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ebaki</ms><mo> </mo><ms>egiten</ms><mo> </mo><ms>dira</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>derantzuna</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Paraleloak</ms><mo> </mo><ms>dira</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Matematika II 3x3ko matrize baten alderantzizkoa Kalkulatu ondoko matrizearen alderantzizkoa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mi»#matrizea«/mi»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»A«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math» matrizearen elementuak:

a₁₁={#1} a₁₂={#2} a₁₃={#3}

a₂₁={#4} a₂₂={#5} a₂₃={#6}

a₃₁={#7} a₃₂={#8} a₃₃={#9}

]]> 9.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>matrizea</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>determinante</mi><mo>(</mo><mi>matrizea</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>x11</mi></mtd><mtd><mi>x12</mi></mtd><mtd><mi>x13</mi></mtd></mtr><mtr><mtd><mi>x21</mi></mtd><mtd><mi>x22</mi></mtd><mtd><mi>x23</mi></mtd></mtr><mtr><mtd><mi>x31</mi></mtd><mtd><mi>x32</mi></mtd><mtd><mi>x33</mi></mtd></mtr></mtable></mfenced><mo>=</mo><msup><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> 4x4ko detereminantea Kalkulatu ondoko matrizearen determinantea:

A = #matrizea

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mi»A«/mi»«/mfenced»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«/math»{#1}

]]> 1.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>matrizea</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>c</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emaitza</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>matrizea</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> bektore elkartzutak (3D) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»#u1«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»#u2«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»m«/mi»«mo»)«/mo»«/math» eta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»m«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»#v2«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»#v3«/mi»«mo»)«/mo»«/math» bektoreak ortogonalak izateko m = {#1} izan beharko da.

f(x) = #funtzioa

]]> 1.0000000 1.0000000 0 true true none #deribatua #funtzio1 #funtzio2 #funtzio3 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>+</mo><mi>sen</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><mi>ln</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><mi>ln</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><msup><exponentiale/><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>+</mo><mi>ln</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>*</mo><msup><exponentiale/><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><mo>(</mo><msup><exponentiale/><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>*</mo><mi>ln</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo><mo>+</mo><mo>(</mo><msup><exponentiale/><mrow><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mo>)</mo><mo>&apos;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deribatua</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>34</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> Buruketa Irekia Ondoko sare honek 20 erpin ditu (5x4)

Ondoko sare honek 8 erpin ditu (2x4)

Zenbat erpin izango ditu 99 lerro eta 9 zutabe dituen sare batek?

]]> 1.0000000 0.0000000 0 editor 15 0 <question/> Distantzia: puntua eta planoa Kalkulatu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Q«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»q«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»q«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»q«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/math» puntutik ondoko π planora dagoen distantzia:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mn»0«/mn»«/math»

Distantzia (Q,π) = {#1} #emaitza

(Oharra: emaitza bi hamartarrekin idatzi eta puntu batez, adibidez: 3.64, kontuz borobiltzerakoan)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»#a11«/mi»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#a12«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#a13«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#b1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a21«/mi»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#a22«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#a23«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#b2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#a31«/mi»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mi»#a32«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»#a33«/mi»«mo»*«/mo»«mi»z«/mi»«mo»=«/mo»«mi»#b3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

x={#1}

y={#2}

z={#3}

]]> 6.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a13</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a21</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a23</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a31</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a32</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a33</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>xemaitza</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>yemaitza</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>zemaitza</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a11</mi><mo>*</mo><mi>xemaitza</mi><mo>+</mo><mi>a12</mi><mo>*</mo><mi>yemaitza</mi><mo>+</mo><mi>a13</mi><mo>*</mo><mi>zemaitza</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a21</mi><mo>*</mo><mi>xemaitza</mi><mo>+</mo><mi>a22</mi><mo>*</mo><mi>yemaitza</mi><mo>+</mo><mi>a23</mi><mo>*</mo><mi>zemaitza</mi></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>a31</mi><mo>*</mo><mi>xemaitza</mi><mo>+</mo><mi>a32</mi><mo>*</mo><mi>yemaitza</mi><mo>+</mo><mi>a33</mi><mo>*</mo><mi>zemaitza</mi></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> jarraitasuna 2 Kalkulatu a-ren balioa ondoko funtzioa jarraitua izan dadin:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»#b«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mi»#d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mi»#d«/mi»«mo»§#160;«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

a = {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»#h«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mi»#d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»#d«/mi»«mo»§lt;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mi»#e«/mi»«mo»§#160;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»#i«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8805;«/mo»«mi»#e«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

a = {#1}

b = {#2}

Ondoko funtzio hau:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»11«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»12«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#8800;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»f«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»d«/mi»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

jarraitua da puntu honetan?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/math»

#graf

Baieztatu L'Hôpitalen Erregela erabiliz

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munder»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»11«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»12«/mn»«/mrow»«/mfrac»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munder»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»112«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»122«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»?«/mo»«mo»?«/mo»«mo»?«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mi»A«/mi»«mi»I«/mi»«mo»§#8201;«/mo»«mo»/«/mo»«mo»§#8201;«/mo»«mi»E«/mi»«mi»Z«/mi»«/math»

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>:</mo><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi><mo>=</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>e</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f112</mi><mo>=</mo><mi>f11</mi><mo>'</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f12</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f122</mi><mo>=</mo><mi>f12</mi><mo>'</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>e</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>)</mo></mrow><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>e</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fa</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x</mi><mo>=</mo><mi>a</mi></mrow><mi>fa</mi><mi>f1</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>g</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>,</mo><mi>p</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>g</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>faltsu</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Konposaketaren deribatua Zein da honako funtzioaren deribatua?

f(x) = #funtzioa

]]> 1.0000000 1.0000000 0 true true none #deribatua #funtzio1 #funtzio2 #funtzio3 <question><wirisCasSession><session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>sen</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mo>-</mo><mi>cos</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>cos</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mi>sen</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mi>sen</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>sen</mi><mo>(</mo><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><msup><exponentiale/><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><msup><exponentiale/><mrow><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mrow></msup></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><mi>ln</mi><mo>(</mo><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aukera</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>ln</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>deribatua</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mtd></mtr><mtr><mtd><mi>funtzio1</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio2</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>funtzio3</mi><mo>=</mo><msup><mi>e</mi><mrow><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>&apos;</mo></mrow></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aukera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>deribatua</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><exponentiale/><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzio3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> KURBA BATEN ZUZEN UKITZAILEAK Erlazionatu ondoko funtzio honen zuzen ukitzaileak emandako abzisa puntuekin

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8201;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

]]> 1.0000000 0.3333333 0 true Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/math»

#graf1

]]> #eku1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/math»

#graf2

]]> #eku2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«/math»

#graf3

]]> #eku3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»4«/mn»«/math»

#graf4

]]> #eku4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x1</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x2</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x3</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x4</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>grafikoa</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku1</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku3</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku4</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> KURBA BATEN ZUZEN UKITZAILEAK 2 Erlazionatu ondoko funtzio honen zuzen ukitzaileak emandako abzisa puntuekin

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

]]> 1.0000000 0.3333333 0 true Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/math»

#graf1

]]> #eku1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/math»

#graf2

]]> #eku2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«/math»

#graf3

]]> #eku3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»4«/mn»«/math»

#graf4

]]> #eku4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo> </mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x1</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x2</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x3</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x4</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>grafikoa</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku1</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku3</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku4</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> KURBA BATEN ZUZEN UKITZAILEAK 3 Erlazionatu ondoko funtzio honen zuzen ukitzaileak emandako abzisa puntuekin

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

]]> 1.0000000 0.3333333 0 true Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/math»

#graf1

]]> #eku1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/math»

#graf2

]]> #eku2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«/math»

#graf3

]]> #eku3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»4«/mn»«/math»

#graf4

]]> #eku4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>8</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d</mi><mo>*</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>d</mi><mo>*</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x1</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x2</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x3</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x4</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>grafikoa</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku1</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku3</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku4</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>7</mn><mn>8</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>8</mn><mn>49</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>68</mn><mn>49</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> KURBA BATEN ZUZEN UKITZAILEAK 4 Erlazionatu ondoko funtzio honen zuzen ukitzaileak emandako abzisa puntuekin

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

]]> 1.0000000 0.3333333 0 true Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/math»

#graf1

]]> #eku1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/math»

#graf2

]]> #eku2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«/math»

#graf3

]]> #eku3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»4«/mn»«/math»

#graf4

]]> #eku4 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>4</mn><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>zentroa</mi><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>zabalera</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>altuera</mi><mo>=</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>ausazko</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ausazko</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>funtzioa</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mi>x1</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>x2</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x3</mi><mo>)</mo><mo>*</mo><mi>x3</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>ff</mi><mo>(</mo><mi>x4</mi><mo>)</mo><mo>*</mo><mi>x4</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>x4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>grafikoa</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku1</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf2</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku2</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf3</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku3</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf4</mi><mo>=</mo><mi>marraztu</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>{</mo><mi>f</mi><mo>,</mo><mi>eku4</mi><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>7</mn><mn>8</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eku4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>8</mn><mn>49</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>68</mn><mn>49</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Matrize baten determinantea Kalkulatu matrize honen determinantea #m.

]]> Aurrera!

]]> 1.0000000 0.1000000 0 0 #sol Zorionak!

2.- Kalkulatu "a" M matrizearen heina 3 ez izateko

Hein(M)=3 bada a-ren edozein baliotarako idatzi EDOZEIN

]]> 1.0000000 0.3333333 0 0 M=#dma =#sol]]> <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>{</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>a</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>dm</mi><mo>=</mo><mfenced close="|" open="|"><mi>M</mi></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>ebatz</mi><mfenced><mrow><mi>dm</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>sol1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>dm</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>"</mo><mi>EDOZEIN</mi><mo>"</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn><mo>*</mo><mi>a</mi></mtd><mtd><mn>4</mn><mo>*</mo><mi>a</mi></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>dm</mi><mn>1</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>EDOZEIN</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mi>M</mi></mfenced><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>m</mi><mspace linebreak="newline"/><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50% 50%</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> OPTIMIZAZIOA 1 #soka metro luzera duen soka luze batekin ikastetxe bateko ikasleek laukizuzen baten itxura duen eremu bat itxi nahi dute frontoiko horma baten ondoan, irudiak adierazten duen moduan:

Horma bakar bat aprobetxatuz lortu daitekeen laukizuzenaren azalerarik handiena m² -tan hauxe da:

]]> 1.0000000 0.3333333 0 true true none Zure erantzuna zuzena da.

]]> Zure galdera zuzena da neurri batean.

]]> Zure erantzuna ez da zuzena

]]> #sol

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

y={#1}x+{#2}

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>pol</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>pol</mi><mo>'</mo><mo>(</mo><mi>xo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>pol</mi><mo>(</mo><mi>xo</mi><mo>)</mo><mo>-</mo><mi>pol</mi><mo>'</mo><mo>(</mo><mi>xo</mi><mo>)</mo><mo>*</mo><mo> </mo><mi>xo</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> parabola baten zuzen ukitzailea x emanda- quizzes Bilatu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«/math» funtzioaren zuzen ukitzailea x=#xo baliorako.

y={#1}x+{#2}

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>pol</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>pol</mi><mo>'</mo><mo>(</mo><mi>xo</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>pol</mi><mo>(</mo><mi>xo</mi><mo>)</mo><mo>-</mo><mi>pol</mi><mo>'</mo><mo>(</mo><mi>xo</mi><mo>)</mo><mo>*</mo><mo> </mo><mi>xo</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> PLANO BATEN EKUAZIOA «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»i«/mi»«mi»r«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»u«/mi»«mi»e«/mi»«mi»k«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»u«/mi»«mi»t«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»l«/mi»«mi»a«/mi»«mi»n«/mi»«mi»o«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»k«/mi»«mi»u«/mi»«mi»a«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»r«/mi»«mi»o«/mi»«mi»k«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»a«/mi»«mo»:«/mo»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»P«/mi»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»Q«/mi»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»R«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»a«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mo»+«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«/math»

#graf

b = {#1}

c = {#2}

d = {#3}

Zein da planoarekiko bektore perpendikularra?

{#4} ·i + {#5} · j + {#6} · k

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="eu">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>geometria_egoera</mi><mfenced><mtext>"3D"</mtext></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>T</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>leiho_altuera</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>leiho_zabalera</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>erakutsi_kubo</mi><mo>=</mo><mi>faltsu</mi><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>:</mo><mo>=</mo><mo>[</mo><msub><mi>Q</mi><mn>1</mn></msub><mo>-</mo><msub><mi>P</mi><mn>1</mn></msub><mo>,</mo><msub><mi>Q</mi><mn>2</mn></msub><mo>-</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><msub><mi>Q</mi><mn>3</mn></msub><mo>-</mo><msub><mi>P</mi><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>:</mo><mo>=</mo><mo>[</mo><msub><mi>R</mi><mn>1</mn></msub><mo>-</mo><msub><mi>P</mi><mn>1</mn></msub><mo>,</mo><msub><mi>R</mi><mn>2</mn></msub><mo>-</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><msub><mi>R</mi><mn>3</mn></msub><mo>-</mo><msub><mi>P</mi><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PX</mi><mo>:</mo><mo>=</mo><mo>[</mo><mi>x</mi><mo>-</mo><msub><mi>P</mi><mn>1</mn></msub><mo>,</mo><mi>y</mi><mo>-</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><mi>z</mi><mo>-</mo><msub><mi>P</mi><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>u</mi><mo>×</mo><mi>v</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>PX</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>p</mi><mo>,</mo><mo>{</mo><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>p</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>P</mi><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>P</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>Q</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>R</mi><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>R</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>marraztu3d</mi><mo>(</mo><mo>{</mo><mi>T</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mi>R</mi><mo>,</mo><mi>p</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>leiho_altuera</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>leiho_zabalera</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>erakutsi_kubo</mi><mo>=</mo><mi>faltsu</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>P</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>Q</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>R</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>p</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>idatzi3d</mi><mo>(</mo><mo>"</mo><mi>P</mi><mo>=</mo><mo>"</mo><mo>|</mo><mi>P</mi><mo>,</mo><mi>P</mi><mo>+</mo><mi>puntu</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo>{</mo><mi>letra_tamaina</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>idatzi3d</mi><mo>(</mo><mo>"</mo><mi>Q</mi><mo>=</mo><mo>"</mo><mo>|</mo><mi>Q</mi><mo>,</mo><mi>Q</mi><mo>+</mo><mi>puntu</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo>{</mo><mi>letra_tamaina</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>idatzi3d</mi><mo>(</mo><mo>"</mo><mi>R</mi><mo>=</mo><mo>"</mo><mo>|</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>+</mo><mi>puntu</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo>{</mo><mi>letra_tamaina</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><msub><mi>P</mi><mn>2</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>2</mn></msub></mtd><mtd><msub><mi>P</mi><mn>3</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>P</mi><mn>2</mn></msub><mo>-</mo><msub><mi>R</mi><mn>2</mn></msub></mtd><mtd><msub><mi>P</mi><mn>3</mn></msub><mo>-</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mo>-</mo><mfenced close="|" open="|"><mtable><mtr><mtd><msub><mi>P</mi><mn>1</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>1</mn></msub></mtd><mtd><msub><mi>P</mi><mn>3</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>P</mi><mn>1</mn></msub><mo>-</mo><msub><mi>R</mi><mn>1</mn></msub></mtd><mtd><msub><mi>P</mi><mn>3</mn></msub><mo>-</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><msub><mi>P</mi><mn>1</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>1</mn></msub></mtd><mtd><msub><mi>P</mi><mn>2</mn></msub><mo>-</mo><msub><mi>Q</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>P</mi><mn>1</mn></msub><mo>-</mo><msub><mi>R</mi><mn>1</mn></msub></mtd><mtd><msub><mi>P</mi><mn>2</mn></msub><mo>-</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd</mi><mo>=</mo><mo>-</mo><msub><mi>P</mi><mn>1</mn></msub><mo>*</mo><mi>aa</mi><mo>-</mo><msub><mi>P</mi><mn>2</mn></msub><mo>*</mo><mi>bb</mi><mo>-</mo><msub><mi>P</mi><mn>3</mn></msub><mo>*</mo><mi>cc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bo</mi><mo>=</mo><mo>-</mo><mi>bb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi><mo>=</mo><mo>-</mo><mi>cc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>do</mi><mo>=</mo><mo>-</mo><mi>dd</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bt</mi><mo>=</mo><mi>cc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ct</mi><mo>=</mo><mi>dd</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dt</mi><mo>=</mo><mi>bb</mi></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Puntu baten simetrikoa plano batekiko «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»K«/mi»«mi»a«/mi»«mi»l«/mi»«mi»k«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mo»#«/mo»«mi»P«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»u«/mi»«mi»r«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»n«/mi»«mi»d«/mi»«mi»o«/mi»«mi»k«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»l«/mi»«mi»a«/mi»«mi»n«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»k«/mi»«mi»i«/mi»«mi»k«/mi»«mi»o«/mi»«mo»:«/mo»«mo»#«/mo»«mi»p«/mi»«mspace linebreak=¨newline¨/»«mi»E«/mi»«mi»r«/mi»«mi»a«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»u«/mi»«mi»n«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»tan«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»,«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

#GRAF

{#1}

]]> 1.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="eu" version="2.0"><library closed="false"><mtext style="color:#ffc800">liburutegia</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>geometria_egoera</mi><mfenced><mtext>"3D"</mtext></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>T</mi><mo>=</mo><mi>tabloia</mi><mo>(</mo><mo>{</mo><mi>leiho_altuera</mi><mo>=</mo><mn>800</mn><mo>,</mo><mi>leiho_zabalera</mi><mo>=</mo><mn>800</mn><mo>,</mo><mi>erakutsi_kubo</mi><mo>=</mo><mi>faltsu</mi><mo>}</mo><mo>)</mo><mo>;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>ausazko</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mo>[</mo><msub><mi>Q</mi><mn>1</mn></msub><mo>-</mo><msub><mi>P</mi><mn>1</mn></msub><mo>,</mo><msub><mi>Q</mi><mn>2</mn></msub><mo>-</mo><msub><mi>P</mi><mn>2</mn></msub><mo>,</mo><msub><mi>Q</mi><mn>3</mn></msub><mo>-</mo><msub><mi>P</mi><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>P</mi><mo>+</mo><mi>Q</mi><mo>)</mo><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PX</mi><mo>:</mo><mo>=</mo><mo>[</mo><mi>x</mi><mo>-</mo><msub><mi>E</mi><mn>1</mn></msub><mo>,</mo><mi>y</mi><mo>-</mo><msub><mi>E</mi><mn>2</mn></msub><mo>,</mo><mi>z</mi><mo>-</mo><msub><mi>E</mi><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>PX</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>GRAF</mi><mo>=</mo><mi>marraztu3d</mi><mo>(</mo><mo>{</mo><mi>T</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mi>p</mi><mo>}</mo><mo>,</mo><mo>{</mo><mo>{</mo><mi>leiho_altuera</mi><mo>=</mo><mn>800</mn><mo>,</mo><mi>leiho_zabalera</mi><mo>=</mo><mn>800</mn><mo>,</mo><mi>erakutsi_kubo</mi><mo>=</mo><mi>faltsu</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>P</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>gorria</mi><mo>}</mo><mo>,</mo><mo>{</mo><mi>kolorea</mi><mo>=</mo><mi>urdin</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>p</mi><mo>}</mo><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>:</mo><mo>=</mo><mi>puntu</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mfrac><mrow><mo>(</mo><mo>-</mo><msub><mi>n</mi><mn>1</mn></msub><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><msub><mi>E</mi><mn>1</mn></msub><mo>)</mo><mo>-</mo><msub><mi>n</mi><mn>2</mn></msub><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><msub><mi>E</mi><mn>2</mn></msub><mo>)</mo><mo>+</mo><msub><mi>n</mi><mn>3</mn></msub><mo>*</mo><msub><mi>E</mi><mn>3</mn></msub><mo>)</mo></mrow><msub><mi>n</mi><mn>3</mn></msub></mfrac><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>X</mi><mo>,</mo><mo>{</mo><mi>tamainu_puntu</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>laranja</mi><mo>,</mo><mi>etiketa</mi><mo>=</mo><mo>"</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>"</mo><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>P</mi><mo>,</mo><mo>{</mo><mi>tamainu</mi><mo>=</mo><mn>14</mn><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>etiketa</mi><mo>=</mo><mi>n</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo>[</mo><mo>-</mo><msub><mi>E</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>1</mn></msub><mo>,</mo><mo>-</mo><msub><mi>E</mi><mn>2</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub><mo>,</mo><mo>-</mo><msub><mi>E</mi><mn>3</mn></msub><mo>+</mo><msub><mi>X</mi><mn>3</mn></msub><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>marraztu3d</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>E</mi><mo>,</mo><mo>{</mo><mi>tamainu</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>lerro_zabalera</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>kolorea</mi><mo>=</mo><mi>laranja</mi><mo>}</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>idatzi3d</mi><mo>(</mo><mo>"</mo><mi>P</mi><mo>=</mo><mo>"</mo><mo>|</mo><mi>P</mi><mo>,</mo><mi>P</mi><mo>+</mo><mi>puntu</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo>{</mo><mi>letra_tamaina</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>GRAF</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tabloia1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>

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Kalkulatu c distantziaren luzera

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#grafikoa

#graf1

#graf2

#graf3

#graf4

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

#graf1

#graf2

#graf3

#graf4

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#grafikoa

#graf1

#graf2

#graf3

#graf4

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»z«/mi»«mi»i«/mi»«mi»o«/mi»«mi»a«/mi»«/math»

#grafikoa

#graf1

#graf2

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#graf4

Horma bakar bat aprobetxatuz lortu daitekeen laukizuzenaren azalerarik handiena m2 -tan hauxe da:

Horma bakar bat aprobetxatuz lortu daitekeen laukizuzenaren azalerarik handiena m² -tan hauxe da:

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