1rBTX 05. SUCCESSIONS/1.5.1 Definició i monotonia 1.5.1.11Q Calcular alguns termes Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è


Format de la resposta: nombre decimal arrodonit als mil·lèsims

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_s]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>12</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.222</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.24</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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#8201;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.1.12Q Calcular alguns termes Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è


Format de la resposta: nombre decimal arrodonit als mil·lèsims

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_s]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>12</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.222</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.24</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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#8201;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.1.13Q CalcularAlgunsTermes Amb la successió an = #a_n

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è


Format de la resposta: nombre decimal arrodonit als mil·lèsims



]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_s]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><msup><mi>n</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>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.995</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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#8201;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.1.14Q CalcularAlgunsTermes Amb la successió an = #a_n

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è


Format de la resposta: nombre decimal arrodonit als mil·lèsims



]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_s]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><msup><mi>n</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>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.995</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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#8201;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.1.15Q CalcularTermeSegüent Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Calcula el terme següent.

 

Format de la resposta: fracció



]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mi>x</mi><mrow><mi>x</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>f</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>f</mi><mo>(</mo><mn>5</mn><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"><mfrac><mi>x</mi><mrow><mi>x</mi><mo>-</mo><mn>6</mn></mrow></mfrac></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"><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></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><mfrac><mn>1</mn><mn>2</mn></mfrac></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"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</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>#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">10</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> Cal prestar atenció per determinar les seqüències. Cal vigiliar perquè es pot haver produït alguna simplificació del tipus 3/6 a 1/2.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.5.1.16Q CalcularTermeSegüent Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Calcula el terme següent.

 

Format de la resposta: fracció



]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mi>x</mi><mrow><mi>x</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>f</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>f</mi><mo>(</mo><mn>5</mn><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"><mfrac><mi>x</mi><mrow><mi>x</mi><mo>-</mo><mn>6</mn></mrow></mfrac></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"><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></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><mfrac><mn>1</mn><mn>2</mn></mfrac></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"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</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>#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">10</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> Cal prestar atenció per determinar les seqüències. Cal vigiliar perquè es pot haver produït alguna simplificació del tipus 3/6 a 1/2.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.5.1.21Q TrobarTermeGeneralRacG1G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»?

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]]> 1.0000000 0.5000000 0 0 #r_18]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>7</mn></mfrac><mo>,</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>,</mo><mfrac><mn>16</mn><mn>9</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></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"><mo>#</mo><mi>r</mi><mo>_</mo><mn>18</mn></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> Cal anar experimentant. El numerador de la fracció és n2

]]> 1.5.1.22Q TrobarTermeGeneralRacG1G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»?

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]]> 1.0000000 0.5000000 0 0 #r_18]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>7</mn></mfrac><mo>,</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>,</mo><mfrac><mn>16</mn><mn>9</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>n</mi><mn>2</mn></msup><mrow><mi>n</mi><mo>+</mo><mn>5</mn></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"><mo>#</mo><mi>r</mi><mo>_</mo><mn>18</mn></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> Cal anar experimentant. El numerador de la fracció és n2

]]> 1.5.1.23Q TrobarTermeGeneralRacG1G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«/mrow»«/mstyle»«/math» ?

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]]> 1.0000000 0.5000000 0 0 #r_18]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>8</mn><mn>7</mn></mfrac><mo>,</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>,</mo><mfrac><mn>10</mn><mn>9</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></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"><mo>#</mo><mi>r</mi><mo>_</mo><mn>18</mn></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">8</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> El numerador de la fracció és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«/mstyle»«/math».

El denominador és semblant.

]]> 1.5.1.24Q TrobarTermeGeneralRacG1G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«/mrow»«/mstyle»«/math» ?

]]>  

]]> 1.0000000 0.5000000 0 0 #r_18]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>8</mn><mn>7</mn></mfrac><mo>,</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>,</mo><mfrac><mn>10</mn><mn>9</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_18</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>5</mn></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"><mo>#</mo><mi>r</mi><mo>_</mo><mn>18</mn></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">8</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> El numerador de la fracció és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«/mstyle»«/math».

El denominador és semblant.

]]> 1.5.1.25Q TrobarTermeGeneralRacG2G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»?

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b_1</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mn>2</mn><mo>,</mo><mfrac><mn>23</mn><mn>8</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"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></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>#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">8</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> El numerador de la fracció es calcula amb n2, del tipus n2+1

el denominador és de primer grau del tipus n+1

si proves per n=1, 2, 3 segur que ho identifiques

]]> 1.5.1.26Q TrobarTermeGeneralRacG2G1 Quin és el terme general de la successió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mrow»«/mstyle»«/math»?

]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</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>b_2</mi><mo>=</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b_1</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>f</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>,</mo><mi>a_4</mi><mo>,</mo><mi>a_5</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mn>2</mn><mo>,</mo><mfrac><mn>23</mn><mn>8</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"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></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>#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">8</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> El numerador de la fracció es calcula amb n2, del tipus n2+1

el denominador és de primer grau del tipus n+1

si proves per n=1, 2, 3 segur que ho identifiques

]]> 1.5.1.30DT MONOTONIA  

Successions creixents

En una successió creixent, el terme següent sempre és més gran que l'anterior. Per això, si an és un terme qualsevol, i an+1 l'immediatament posterior, la  successió és creixent si

an+1 - an > 0
Successions decreixents

Una successió és decreixent si

an+1 - an < 0
]]> 0.0000000 0.0000000 0 1.5.1.31Q MonotoniaPolinomiG1 Considera la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«/mstyle»«/math»

a) Calcula an+1  
Format de la resposta (n+1)^2/(2n+3)

b) Calcula an+1 - an 

c) És creixent la successió (S/N) ?


]]> 1.0000000 0.3333333 0 0 a) =#an1b) =#adc) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>aleatori</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>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>aleatori</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><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ad</mi><mo>=</mo><mi>an1</mi><mo>-</mo><mi>an</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>ad</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mi>S</mi><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mi>N</mi><mo>&quot;</mo></mrow></apply></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>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ad</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>N</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"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>n</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi mathvariant="normal">d</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><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">8</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula an+1  substituint n per n+1 en l'expressió de an .

Resta an+1 - an

Estudia el signe del resultat

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»an«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 1.5.1.32Q Monotonia RacionalG1G1 Considera la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

a) Calcula an+1  
Format de la resposta (n+1)^2/(2n+3)

b) Calcula an+1 - an 

c) És creixent la successió (S/N) ?


]]> 1.0000000 0.3333333 0 0 a) =#a_pb) =#a_qc) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</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>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>-</mo><mi>b_3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mi>a_p</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>S</mi></math></input></command></group></library><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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1.5.1.33Q Monotonia RacionalG1G1 Considera la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

a) Calcula an+1  
Format de la resposta (n+1)^2/(2n+3)

b) Calcula an+1 - an 

c) És creixent la successió (S/N) ?


]]> 1.0000000 0.3333333 0 0 a) =#a_pb) =#a_qc) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</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>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>-</mo><mi>b_3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mi>a_p</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>S</mi></math></input></command></group></library><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>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1.5.1.34Q MonotoniaRacionalG2G1 Considera la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

a) Calcula an+1  
Format de la resposta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mo»(«/mo»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/mrow»«mrow»«mn»2«/mn»«mi»n«/mi»«mo»+«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

b) Calcula an+1 - an 

c) És creixent la successió (S/N) ?


]]> 1.0000000 0.5000000 0 0 a) =#sol1b) =#sol2c) =#sol3]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</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>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</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>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><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>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>sol1</mi><mo>-</mo><mi>a_n</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>b1</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mo>&quot;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo>&nbsp;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo>&nbsp;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr></mtable></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></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></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"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></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"><mfrac><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>13</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>35</mn></mrow></mfrac></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"><mi>S</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>u1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>és</ms><mo>,</mo><ms>és</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"><mi>a</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per calcular an+1,has de substituir n per n+1:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Atenció: (n+1)2 = n2 + 2n + 1

Com que la diferència an+1 - an #t1 positiva, la successió #u1 creixent

]]> 1.5.1.35Q MonotoniaRacionalG2G1 Considera la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

a) Calcula an+1  
Format de la resposta (n+1)^2/(2n+3)

b) Calcula an+1 - an 

c) És creixent la successió (S/N) ?


]]> 1.0000000 0.5000000 0 0 a) =#a_pb) =#a_qc) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</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>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</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>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mi>a_p</mi><mo>-</mo><mi>a_n</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>b1</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mo>&quot;</mo><mi>és</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo> </mo><mi>és</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mo>&quot;</mo><mi>no</mi><mo> </mo><mi>és</mi><mo>&quot;</mo></mtd></mtr></mtable></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></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>35</mn></mrow></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"><mi>N</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>u1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>no</ms><mo> </mo><ms>és</ms><mo>,</mo><ms>no</ms><mo> </mo><ms>és</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"><mi>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que la diferència an+1 - an #t1 positiva, la successió #u1 creixent

]]> 1.5.1.60DT FITA SUP/INF  

Fita superior 

F és fita superior de la successió an si, i només si, F ≥ an, per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8704;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/math».

Es demostra comprovant que F - an ≥ 0
Fita inferior

f és fita inferior de la successió an si, fi només si, f ≤ an, per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8704;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/math»

Es demostra comprovant que f - an ≤ 0
 
]]> 0.0000000 0.0000000 0 1.5.1.61Q FitaSuperior Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»el«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nombre«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«/mrow»«/mstyle»«/math»

a) Calcula F - an: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math».  Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»6«/mn»«mrow»«mn»3«/mn»«mi»n«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math» és fita superior? (S/N) 




]]> 1.0000000 0.5000000 0 0 a) =#a_pb) =#m_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>t</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>b_4</mi><mo>-</mo><mi>b_1</mi><mo>*</mo><mi>b_2</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>u</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>N</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>S</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>m</mi><mi>_</mi><mn>1</mn></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> Esbrina el signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a_p«/mi»«/mrow»«/mstyle»«/math»

]]> 1.5.1.62Q FitaSuperior Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»el«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»nombre«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«/mrow»«/mstyle»«/math»

a) Calcula F - an: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math».  Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»6«/mn»«mrow»«mn»3«/mn»«mi»n«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math» és fita superior? (S/N) 




]]> 1.0000000 0.5000000 0 0 a) =#a_pb) =#m_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>t</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>b_4</mi><mo>-</mo><mi>b_1</mi><mo>*</mo><mi>b_2</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>u</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>N</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>S</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>#</mo><mi>m</mi><mi>_</mi><mn>1</mn></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> Esbrina el signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a_p«/mi»«/mrow»«/mstyle»«/math»

]]> 1.5.1.63Q FitaInferior Amb la successió  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»l«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»o«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»m«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math»

a) Calcula f - an: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math».  Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»6«/mn»«mrow»«mn»3«/mn»«mi»n«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math» és fita inferior? (S/N) 




]]> 1.0000000 0.5000000 0 0 a) =#a_pb) =#m_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>t</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>b_4</mi><mo>-</mo><mi>b_1</mi><mo>*</mo><mi>b_2</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>u</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>N</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>S</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>m</mi><mi>_</mi><mn>1</mn></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">8</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> Esbrina el signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a_p«/mi»«/mrow»«/mstyle»«/math»

]]> 1.5.1.64Q FitaInferior Amb la successió  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»l«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»o«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»m«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math»

a) Calcula f - an: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math».  Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»6«/mn»«mrow»«mn»3«/mn»«mi»n«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»t«/mi»«/mstyle»«/math» és fita inferior? (S/N) 




]]> 1.0000000 0.5000000 0 0 a) =#a_pb) =#m_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><naturalnumbers/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>t</mi><mo>-</mo><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mi>b_4</mi><mo>-</mo><mi>b_1</mi><mo>*</mo><mi>b_2</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>u</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>N</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>m_1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mi>S</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>m</mi><mi>_</mi><mn>1</mn></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">8</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> Esbrina el signe de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a_p«/mi»«/mrow»«/mstyle»«/math»

]]> 1rBTX 05. SUCCESSIONS/1.5.2 Operacions amb successions 1.5.2.10DT OPERACIONS AMB SUCCESSIONS Operacions amb successions

Per a sumar-les, sumem els seus termes generals.

Per a restar-les, restem els seus termes generals.

Per a multiplicar-les, multipliquem els seus termes generals.

 

 

 

 
]]> 0.0000000 0.0000000 0 1.5.2.11Q SumaSuccessions Considera les successions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Dona l'expressió simplificada de la suma an + bn.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>na</mi><mo>=</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></mtd></mtr><mtr><mtd><mi>da</mi><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b_2</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>nb</mi><mo>=</mo><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_3</mi></mtd></mtr><mtr><mtd><mi>db</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>b_2</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mfenced><mrow><mi>na</mi><mo>,</mo><mi>da</mi></mrow></mfenced><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mfenced><mrow><mi>nb</mi><mo>,</mo><mi>db</mi></mrow></mfenced><mo>=</mo><mn>1</mn></mrow></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mi>b_1</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b_2</mi></mfenced><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_3</mi></mrow><mrow><mi>n</mi><mo>-</mo><mi>b_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a_n</mi><mo>+</mo><mi>b_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m12</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>da</mi><mo>,</mo><mi>db</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m12</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m21</mi><mo>=</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>,</mo><mi>b_7</mi><mo>,</mo><mi>b_8</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>,</mo><mi>b_7</mi><mo>,</mo><mi>b_8</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>36</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mn>6</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>+</mo><mn>6</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"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>54</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>33</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>36</mn></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>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> Es tracta de sumar fraccions algèbriques: cal reduir-les al mínim comú denominador.

El denominador comú és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=93951409bf97f62dd21fe76e1eef72a8&cw=40&ch=10&cb=9" width="40" height="10" style="vertical-align: -1px;"/>

]]> Amb el denominador comú, les fraccions es transformen en:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»na«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»nb«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7dec39e8aab119c9eab388e3935f9dc2&cw=219&ch=27&cb=18" width="219" height="27" style="vertical-align: -9px;"/>

]]> 1.5.2.21Q RestaSuccessions Considera les successions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»bn«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Dona l'expressió simplificada de la resta an - bn.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>na</mi><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>da</mi><mo>=</mo><msup><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>nb</mi><mo>=</mo><mi>b4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b3</mi></mtd></mtr><mtr><mtd><mi>db</mi><mo>=</mo><mi>b5</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>na</mi><mo>,</mo><mi>da</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>nb</mi><mo>,</mo><mi>db</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi></mrow><msup><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mn>2</mn></msup></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msup><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b3</mi></mrow><mrow><mi>b5</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b2</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>b5</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bn</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>an</mi><mo>-</mo><mi>bn</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>b5</mi><mo>*</mo><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mo>(</mo><mi>b4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m12</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>da</mi><mo>,</mo><mi>db</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>m12</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>8</mn></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mfenced><mrow><mi>n</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></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"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>26</mn></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>20</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>20</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>n</mi><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><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">8</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> Primer es calcula el denominador comú de les dues fraccions:

  • #d1 = (#d2)2
  • #e1 = #b5 · (#d2)

i el mcm és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=93951409bf97f62dd21fe76e1eef72a8&cw=40&ch=10&cb=9" width="40" height="10" style="vertical-align: -1px;"/>

]]> Si el mcm és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=93951409bf97f62dd21fe76e1eef72a8&cw=40&ch=10&cb=9" width="40" height="10" style="vertical-align: -1px;"/>

Les fraccions equivalents s'escriuen: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»*«/mo»«mfenced»«mrow»«msup»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5b7e1cb596616e7c990a2ffc0eec0122&cw=277&ch=29&cb=20" width="277" height="29" style="vertical-align: -9px;"/>

 i, multiplicant:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=fdd652a25f1786d186e3ab5d4074b262&cw=112&ch=25&cb=16" width="112" height="25" style="vertical-align: -9px;"/>

]]> 1.5.2.31Q ProducteSuccessions Considera les successions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mrow»«/mstyle»«/math»

Dona l'expressió simplificada del producte an · bn.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>na</mi><mo>=</mo><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi><mo>*</mo><mi>b_1</mi></mtd></mtr><mtr><mtd><mi>da</mi><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b_2</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>nb</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>b_2</mi></mtd></mtr><mtr><mtd><mi>db</mi><mo>=</mo><mi>b_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_3</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>na</mi><mo>,</mo><mi>da</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>nb</mi><mo>,</mo><mi>db</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi><mo>*</mo><mi>b_1</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b_2</mi></mfenced><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>-</mo><mi>b_2</mi></mrow><mrow><mi>b_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_3</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a_n</mi><mo>*</mo><mi>b_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nab2</mi><mo>=</mo><mi>na</mi><mo>*</mo><mi>nb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dab2</mi><mo>=</mo><mi>da</mi><mo>*</mo><mi>db</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nab</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>nab2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dab</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>dab2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>24</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>-</mo><mn>2</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>40</mn></mrow></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"><mfrac><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>10</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nab</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dab</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</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>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> Es tracta de multiplicar fraccions algèbriques: cal factoritzar per simplificar.

Un cop multiplicats els numeradors entre ells i els denominadors entre ells, queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»nab«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»dab«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=6ad8c9737e774cb0269731f9b812873d&cw=94&ch=25&cb=16" width="94" height="25" style="vertical-align: -9px;"/>

]]> 1.5.2.41Q QuocientSuccessions Considera les successions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»bn«/mi»«/mrow»«/mstyle»«/math».

Dona l'expressió simplificada del quocient «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b12</mi><mo>=</mo><msup><mi>b2</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>b11</mi><mo>=</mo><msup><mi>b1</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>b4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b12</mi></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>b4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b3</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b1</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b1</mi><mo>)</mo></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b12</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b3</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>b1</mi><mo>)</mo></mrow><mrow><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mi>b1</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bn</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>an</mi><mi>bn</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>49</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>48</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>14</mn></mrow></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"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>n</mi><mo>-</mo><mn>56</mn></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>#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">8</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> Primer es multiplica la primera fracció per la fracció inversa de la segona:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=37e69acd02b4e6ad6e76ff5925871160&cw=92&ch=29&cb=18" width="92" height="29" style="vertical-align: -11px;"/>

i es factoritza per simplificar.

]]> Es factoritza:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=c55cc3329672cdc6db6654c574f97585&cw=91&ch=29&cb=18" width="91" height="29" style="vertical-align: -11px;"/>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=29b4df6bef4a9d6f3a4667817c8232f7&cw=325&ch=30&cb=18" width="325" height="30" style="vertical-align: -12px;"/>

]]> 1.5.2.51Q PotènciaSuccessió Considera la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math»

Doneu l'expressió simplificada de la potència (an)3

]]> 1.0000000 0.5000000 0 0 #r_84 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_6&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_7&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b_8&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mfenced 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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_84 </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> Cal elevar el numerador a 3... i el denominador també!

]]> 1rBTX 05. SUCCESSIONS/1.5.3 Concepte de límit 1.5.3.10DT CONVERGÈNCIA Convergència

Una successió és convergent si, i només si té límit finit.

En cas contrari, és divergent.

 

 

 

 
]]> 0.0000000 0.0000000 0 1.5.3.21Q CalcularTermes+IntuirLimG1G1 Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è

d) intueix quin és el seu límit

Format de la resposta:

a,b,c: nombre decimal arrodonit als mil·lèsims

d: si té límit finit, és un nombre enter; sinó és ±∞

 

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_sd) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>n12</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mfenced><mfenced><mrow><mi>b_1</mi><mo>/</mo><mi>b_3</mi></mrow></mfenced></mfenced><mo>∈</mo><integers/><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n11</mi><mo>,</mo><mi>n12</mi><mo>)</mo><mo>=</mo><mn>1</mn></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">repeat</csymbol><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>1000</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>sol1</mi><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>001</mn><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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>8</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2.667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3.843</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3.984</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"><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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x02009;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.3.22Q CalcularTermes+IntuirLimG2G1 Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è

d) intueix quin és el seu límit

Format de la resposta:

a,b,c: nombre decimal arrodonit als mil·lèsims

d: si té límit finit, és un nombre enter; sinó és ±∞

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_sd) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>1000</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><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">if</csymbol><mrow><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><cn>+∞</cn></mrow><mrow><mi>sol</mi><mo>=</mo><cn>-∞</cn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>001</mn><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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.615</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97.078</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>997.01</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"><cn>+∞</cn></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>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x02009;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-8)</option><option name="relative_tolerance">false</option><option name="precision">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.3.23Q CalcularTermes+IntuirLimG1G2 Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è

d) intueix quin és el seu límit

Format de la resposta:

a,b,c: nombre decimal arrodonit als mil·lèsims

d: si té límit finit, és un nombre enter; sinó és ±∞

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_sd) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>1000</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_p</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>sol1</mi><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>001</mn><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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>8</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.272</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.021</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.002</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></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>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x02009;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.3.25Q CalcularTermes+IntuirLimG2G2 Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è

d) intueix quin és el seu límit

Format de la resposta: 

 

a,b,c: nombre decimal arrodonit als mil·lèsims

d: si té límit finit, és un nombre enter; sinó és ±∞

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_sd) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n11</mi><mo>=</mo><mi>b_1</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b_2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>n12</mi><mo>=</mo><mi>b_3</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced><mrow><mi>b_1</mi><mo>/</mo><mi>b_3</mi></mrow></mfenced><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n11</mi><mo>,</mo><mi>n12</mi><mo>)</mo><mo>=</mo><mn>1</mn></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">repeat</csymbol><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>1000</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>sol1</mi><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5.05</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4.082</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4.008</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"><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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x02009;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><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">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1.5.3.26Q CalcularTermes+IntuirLimG3G2 Amb la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

Calcula els termes demanats:

a) #q è

b) #r è

c) #s è

d) intueix quin és el seu límit

Format de la resposta:

a,b,c: nombre decimal arrodonit als mil·lèsims

d: si té límit finit, és un nombre enter; sinó és ±∞

]]> 1.0000000 0.5000000 0 0 a) =#a_qb) =#a_rc) =#a_sd) =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b_2</mi><mo>/</mo><mi>b_4</mi></mrow></mfenced><mo>∉</mo><integers/></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>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>1000</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_3</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>+</mo><mi>b_4</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>b_2</mi></mrow></mfenced></mrow><mrow><mi>b_3</mi><mo>*</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><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">if</csymbol><mrow><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><cn>+∞</cn></mrow><mrow><mi>sol</mi><mo>=</mo><cn>-∞</cn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>001</mn><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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11.964</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>102.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1002.</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"><cn>+∞</cn></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>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>q</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>r</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x02009;</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal substituir i fer anar la calculadora.

]]> 1rBTX 05. SUCCESSIONS/1.5.4 Lím Succ. Algèbriques 1.5.4.10 TEORIA: LÍMIT DE POLINOMI
 Límit d'un polinomi
 El límit d'un polinomi és el mateix que el del seu terme de grau més alt.
 
 
 

 

 
]]> 0.0000000 0.0000000 0 1.5.4.11Q límit polinomi Calcula el límit de la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfenced><mrow><mi>b_6</mi><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</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"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup></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"><cn>-∞</cn></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que és el límit d'un polinomi, és igual al límit del seu terme de grau més alt: #g1

]]> 1.5.4.15Q LímitPolinomiSigneAleat Calcula el límit de la successió an = #a_n

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfenced><mrow><mi>b_6</mi><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn><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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</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"><cn>+∞</cn></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"><param name="intervals">true</param></assertion><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És el límit d'un polinomi, per tant és igual al límit del seu monomi de grau més alt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msup»«/mrow»«/mstyle»«/math»

]]> 1.5.4.16Q LímitPolinomiSigneAleat_2 Calcula el límit de la successió an = #a_n

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</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>b_6</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></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"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</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"><mo> </mo><ms>-infinit</ms><mo> </mo></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_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És el límit d'un polinomi, per tant és igual al límit del seu monomi de grau més alt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msup»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=55a9b3688cc15b2816588abb397d423e&cw=57&ch=14&cb=13" width="57" height="14" style="vertical-align: -1px;"/>" 

]]> 1.5.4.20DT LÍMIT DE FRACCIONS
 Límit d'una fracció algèbrica
 

Per determinar el límit d'una fracció algèbrica:

  • si el grau del numerador és superior, el límit és infinit.
  • si el grau del denominador és superior, el límit és zero.
  • si els graus són iguals, el límit és el quocient dels coeficients dels termes de grau més alt.
 
 
 

 

 
]]> 0.0000000 0.0000000 0 1.5.4.21Q LímQuocientPolinomis_GrauNumSup Calcula el límit de la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mfrac><mi>b_3</mi><mi>b_1</mi></mfrac></mfenced><mo>≠</mo><mfenced close="|" open="|"><mfrac><mi>b_6</mi><mi>b_3</mi></mfrac></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_4</mi></msup></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</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><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></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"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><ms>-infinit</ms><mo> </mo></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_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És un quocient de polinomis i el grau del numerador és superior. El límit de la successió és igual a: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=284fc888a6fcf0495c26d427d84f93be&cw=239&ch=30&cb=20" width="239" height="30" style="vertical-align: -10px;"/>

]]> 1.5.4.22Q LímQuocientPolinomis_GrauNumSup_2 Calcula el límit de la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mfrac><mi>b_3</mi><mi>b_1</mi></mfrac></mfenced><mo>≠</mo><mfenced close="|" open="|"><mfrac><mi>b_6</mi><mi>b_3</mi></mfrac></mfenced></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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_4</mi></msup></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</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><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></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"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><ms>-infinit</ms><mo> </mo></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_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És un quocient de polinomis i el grau del numerador és superior. El límit de la successió és igual a: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=284fc888a6fcf0495c26d427d84f93be&cw=239&ch=30&cb=20" width="239" height="30" style="vertical-align: -10px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=284fc888a6fcf0495c26d427d84f93be&cw=239&ch=30&cb=20" width="239" height="30" style="vertical-align: -10px;"/>

]]> 1.5.4.25Q LímQuocientPolinomis_GrauDenSup Calcula el límit de la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mrow><mi>b_2</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És el límit d'un quocient de polinomis, i per tant cada polinomi tendeix al límit del seu monomi de grau més alt.

El límit de la successió és: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=702f32bdf70c1f9c67f0a2c6aab42e35&cw=205&ch=33&cb=20" width="205" height="33" style="vertical-align: -13px;"/>" 

]]> 1.5.4.26Q LímQuocientPolinomis_GrauDenSup_2 Calcula el límit de la successió an = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mrow><mi>b_2</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> És el límit d'un quocient de polinomis, i per tant cada polinomi tendeix al límit del seu monomi de grau més alt.

El límit de la successió és: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=702f32bdf70c1f9c67f0a2c6aab42e35&cw=205&ch=33&cb=20" width="205" height="33" style="vertical-align: -13px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=702f32bdf70c1f9c67f0a2c6aab42e35&cw=205&ch=33&cb=20" width="205" height="33" style="vertical-align: -13px;"/>" 

]]> 1.5.4.31Q LímitQuocientPolinomis_MateixGrau Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></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"><mo>-</mo><mfrac><mn>2</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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</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> Com que és un quocient de polinomis, fixa't en els termes de grau més alt.

El límit de la fracció és igual a  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=df3210f12d9fd0f547aa771f9af11316&cw=104&ch=33&cb=20" width="104" height="33" style="vertical-align: -13px;"/> 

que es pot simplificar per  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79193e3c5542210f3aefbd27be317de7&cw=33&ch=14&cb=13" width="33" height="14" style="vertical-align: -1px;"/>

]]> 1.5.4.32Q LímitQuocientPolinomis_MateixGrau_2 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></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"><mo>-</mo><mfrac><mn>2</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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</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> Com que és un quocient de polinomis, fixa't en els termes de grau més alt.

El límit de la fracció és igual a  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=df3210f12d9fd0f547aa771f9af11316&cw=104&ch=33&cb=20" width="104" height="33" style="vertical-align: -13px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=df3210f12d9fd0f547aa771f9af11316&cw=104&ch=33&cb=20" width="104" height="33" style="vertical-align: -13px;"/> 

que es pot simplificar per  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79193e3c5542210f3aefbd27be317de7&cw=33&ch=14&cb=13" width="33" height="14" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79193e3c5542210f3aefbd27be317de7&cw=33&ch=14&cb=13" width="33" height="14" style="vertical-align: -1px;"/>

]]> 1.5.4.41Q LímQuocientPolinomis_Aleatori Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></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"><mi>d</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></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"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>grau</ms><mo> </mo><ms>del</ms><mo> </mo><ms>numerador</ms><mo> </mo><ms>és</ms><mo> </mo><ms>superior</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>límit</ms><mo> </mo><ms>és</ms><mo> </mo><ms>infinit</ms></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> #M1

#M2

]]> 1.5.4.42Q LímQuocientPolinomis_Aleatori_2 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></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"><mi>d</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></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"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>grau</ms><mo> </mo><ms>del</ms><mo> </mo><ms>numerador</ms><mo> </mo><ms>és</ms><mo> </mo><ms>superior</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>límit</ms><mo> </mo><ms>és</ms><mo> </mo><ms>infinit</ms></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">8</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> #M1

#M2

]]> 1.5.4.51Q LímitRestaFraccions:determinat Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>70</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>176</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>90</mn></mrow><mrow><mn>24</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>90</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>81</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>35</mn><mn>12</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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> El límit de la diferència és la diferència dels límits

]]> 1.5.4.61Q LímitProducteFraccions:determinat Calcula el límit de la successió producte:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>·</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>18</mn></mrow><mrow><mn>12</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>18</mn></mrow></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"><mo>-</mo><mfrac><mn>5</mn><mn>6</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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> El límit del producte és el producte  dels límits

]]> 1.5.4.62Q LímitSumaArrels:determinat Calcula el límit de la successió suma:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></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"><cn>+∞</cn></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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> El límit de la suma  és la suma  dels límits

]]> 1.5.4.63Q LímExponencialAleat_Determinat Calcula el límit de la successió exponencial «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>n11</mi><mo>=</mo><mi>n1</mi><mo>*</mo><msup><mi>n</mi><mi>e1</mi></msup><mo>+</mo><mi>n2</mi><mo>*</mo><msup><mi>n</mi><mi>e2</mi></msup><mo>+</mo><mi>n3</mi><mo>*</mo><msup><mi>n</mi><mi>e3</mi></msup></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>d1</mi><mo>*</mo><msup><mi>n</mi><mi>e1</mi></msup><mo>+</mo><mi>d2</mi><mo>*</mo><msup><mi>n</mi><mi>e2</mi></msup><mo>+</mo><mi>d3</mi><mo>*</mo><msup><mi>n</mi><mi>e3</mi></msup></mtd></mtr></mtable><mrow><mi>n1</mi><mo>≠</mo><mi>d1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</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>c12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_n</mi><mo>=</mo><mi>c11</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>c12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mfrac><mi>n11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>:</mo><mo>=</mo><msup><mfenced><mfrac><mi>n11</mi><mi>d11</mi></mfrac></mfenced><mi>c_n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</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>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow><mrow><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></msup></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"><cn>+∞</cn></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">8</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> El límit de la base de l'exponencial és, ja que es tracta d'un quocient de polinomis de mateix grau: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Només falta elevar-la a l'infinit:

  • tenint present el signe de l'infinit de l'exponent
  • tenint present si el resultat és més gran o més petit que 1

 

]]> 1rBTX 05. SUCCESSIONS/1.5.5 Resolució d'indeterminacions 1.5.5.10DT INDETERMINACIONS FRACCIONS
 Indeterminacions amb fraccions
 

Per resoldre les indeterminacions del tipus 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8734;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8734;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»§#8734;«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8734;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8201;«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»0«/mn»«mn mathvariant=¨bold¨»0«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/math»

Es solen efectuar les operacions indicades.

 
 
 
 
 
]]> 0.0000000 0.0000000 0 1.5.5.11Q IndRestaFraccions Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> La 1a fracció té per límit #k1;

la 2a fracció té per límit #k2.

Tenim una indeterminació de tipus -∞+∞ o +∞-∞. Per resoldre, es resten les fraccions algèbriques, calculant el denominador comú de les dues fraccions.

El resultat de la resta és la fracció #a_n i el seu límit s'esbrina mirant els graus i els coeficients del numerador i del denominador.

 

]]> 1.0000000 0.5000000 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>84</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>98</mn></mrow><mrow><mn>21</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>49</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</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>k1</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>k2</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>81</mn></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> La 1a fracció té per límit #k1;

la 2a fracció té per límit #k2.

Tenim una indeterminació de tipus -∞+∞ o +∞-∞. Per resoldre, es resten les fraccions algèbriques, calculant el denominador comú de les dues fraccions.

El resultat de la resta és la fracció #a_n i el seu límit s'esbrina mirant els graus i els coeficients del numerador i del denominador.

 

]]> 1.5.5.20Q IndProducteFraccions Calcula el límit de la successió an = #b_n · #c_n

]]> Cal multiplicar les fraccions; el seu producte és #a_n

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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_81 </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> Cal multiplicar les fraccions; el seu producte és #a_n

]]> 1.5.5.31Q IndQuocientFraccions Calcula el límit de la successió an = #b_n : #c_n

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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_81&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;lim&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;cn&gt;+∞&lt;/cn&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mi&gt;a_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_3&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_4&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_5&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_6&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;135&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;486&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;135&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;486&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;28&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;672&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;162&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2187&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;13122&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_81&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_81 </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> Com que d'entrada, el límit és ∞/∞, cal dividir les fraccions i simplificar; el seu quocient és #a_n.

]]> 1.5.5.40DT INDETERMINACIONS ARRELS
 Indeterminació amb arrel
 

Per resoldre les indeterminacions del tipus «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8734;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8734;«/mo»«/math» amb arrels, es sol multiplicar i dividir pel conjugat.

 
 
 
 
 
]]> 0.0000000 0.0000000 0 1.5.5.41Q RestaArrelsInd_G1 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_2</mi><mo>≠</mo><mi>b_5</mi></mrow></apply><mrow><mi>a_n</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi><mo>=</mo><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n11</mi><mo>-</mo><mi>n12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>n11</mi></msqrt><mo>+</mo><msqrt><mi>n12</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mo>(</mo><mi>b_2</mi><mo>-</mo><mi>b_4</mi><mo>)</mo><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><mi>n</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b_4</mi><mo>*</mo><mi>n</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><msqrt><mi>n</mi></msqrt><mo>*</mo><mfenced><mrow><msqrt><mi>b_2</mi></msqrt><mo>+</mo><msqrt><mi>b_4</mi></msqrt></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>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></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"><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></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>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>81</mn></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">8</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> Cal multiplicar i dividir pel conjugat:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»l«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=40513665c49d266981225cbc390ea76d&cw=257&ch=29&cb=18" width="257" height="29" style="vertical-align: -11px;"/>
i simplificar per trobar el límit.

]]> Efectua:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=68b40d31a93c9a94d3e171be83be4d6d&cw=261&ch=27&cb=18" width="261" height="27" style="vertical-align: -9px;"/>

i, a l'infinit, els límits són equivalents als dels termes de grau més alt

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=3c4618865cd9e6bd9bab634737dbb4c6&cw=179&ch=25&cb=16" width="179" height="25" style="vertical-align: -9px;"/>

]]> 1.5.5.51Q RestaArrelsInd_G2 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_5</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_2</mi><mo>≠</mo><mi>b_5</mi></mrow></apply><mrow><mi>a_n</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n11</mi><mo>-</mo><mi>n12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>n11</mi></msqrt><mo>+</mo><msqrt><mi>n12</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>n</mi><mo>*</mo><mfenced><mrow><msqrt><mi>b_2</mi></msqrt><mo>+</mo><msqrt><mi>b_4</mi></msqrt></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>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></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"><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></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>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>81</mn></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">8</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> Cal multiplicar i dividir pel conjugat:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»l«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=40513665c49d266981225cbc390ea76d&cw=257&ch=29&cb=18" width="257" height="29" style="vertical-align: -11px;"/>
i simplificar per trobar el límit.

]]> Efectua:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=68b40d31a93c9a94d3e171be83be4d6d&cw=261&ch=27&cb=18" width="261" height="27" style="vertical-align: -9px;"/>

i, a l'infinit, els límits són equivalents als dels termes de grau més alt

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=3c4618865cd9e6bd9bab634737dbb4c6&cw=179&ch=25&cb=16" width="179" height="25" style="vertical-align: -9px;"/>

]]> 1.5.5.60DT INDET_e
 1∞
 
Les indeterminacions del tipus 1∞, es resolen amb:
 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»l§#237;m«/mi»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»
 

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8734;«/mo»«/mstyle»«/math»
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mstyle»«/math» 

 
 
 
 
 
 
 
 
]]> 0.0000000 0.0000000 0 1.5.5.61Q IndeterminacióNombre e Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»


]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>=</mo><mn>1</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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</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>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>w3</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>=</mo><mi>grau</mi><mo>(</mo><mi>w4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></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"><mfrac><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</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"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</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>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow><mrow><mn>8</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></msup></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></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">8</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> La successió és del tipus indeterminació 1∞ i es calcula amb el nombre e:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«msup»«mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»lim«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»

El seu límit és: 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8734;«/mo»«/mstyle»«/math»
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mrow»«/mstyle»«/math» 
]]> 1.5.5.62Q Ind_ e_ArrelSimplificable Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»


]]>  

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b2</mi><mo>≠</mo><mi>b4</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>n</mi><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</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>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>w3</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>=</mo><mi>grau</mi><mo>(</mo><mi>w4</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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></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"><mfrac><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</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"><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac><mrow><mi>n</mi><mo>-</mo><mn>4</mn></mrow></msup></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"><mfrac><msup><mroot><exponentiale/><mn>4</mn></mroot><mn>3</mn></msup><exponentiale/></mfrac></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="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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La successió és del tipus indeterminació 1∞ i es calcula amb el nombre e:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«msup»«mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»lim«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»

El seu límit és: 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8734;«/mo»«/mstyle»«/math»
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mrow»«/mstyle»«/math» 

 

]]> 1.5.5.91Q LímitSumaFrac_Indet Calcula límit de la successió an = #b_n - #c_n

]]> La 1a fracció té per límit #k1;

la 2a fracció té per límit #k2.

Tenim una indeterminació de tipus -∞+∞ o +∞-∞. Per resoldre, es resten les fraccions algèbriques, calculant el denominador comú de les dues fraccions.

El resultat de la resta és la fracció #a_n i el seu límit s'esbrina mirant els graus i els coeficients del numerador i del denominador.

 

]]> 1.0000000 0.5000000 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>84</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>98</mn></mrow><mrow><mn>21</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>49</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</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>k1</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>k2</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>81</mn></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> La 1a fracció té per límit #k1;

la 2a fracció té per límit #k2.

Tenim una indeterminació de tipus -∞+∞ o +∞-∞. Per resoldre, es resten les fraccions algèbriques, calculant el denominador comú de les dues fraccions.

El resultat de la resta és la fracció #a_n i el seu límit s'esbrina mirant els graus i els coeficients del numerador i del denominador.

 

]]> 1.5.5.92Q LímitRestaFrac_Indet Calcula el límit de la successió  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>84</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>98</mn></mrow><mrow><mn>21</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>49</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</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>k1</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>k2</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><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>81</mn></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> La 1a fracció té per límit #k1;

la 2a fracció té per límit #k2.

Tenim una indeterminació de tipus -∞+∞ o +∞-∞. Per resoldre, es resten les fraccions algèbriques, calculant el denominador comú de les dues fraccions.

El resultat de la resta és la fracció #a_n i el seu límit s'esbrina mirant els graus i els coeficients del numerador i del denominador.

 

]]> 1.5.5.93Q LímitProdFrac_Indet Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

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]]> 1.5.5.94Q LímitQuocientFrac_Indet Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;135&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;486&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;135&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;486&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_n&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;63&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;28&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;672&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;162&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2187&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;13122&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_81&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_81 </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> Com que d'entrada, el límit és ∞/∞, cal dividir les fraccions i simplificar; el seu quocient és #a_n.

]]> 1.5.5.95Q IndetArrel Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mfrac><mrow><mfenced 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align="center"><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfenced></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_2</mi><mo>≠</mo><mi>b_5</mi></mrow></apply><mrow><mi>a_n</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></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"><mfrac><mrow><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced><mo>*</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mtd></mtr></mtable></mfenced></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></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>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></msqrt></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"><cn>-∞</cn></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar i dividir pel conjugat:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»l«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mfrac»«/mstyle»«/math»


i simplificar per trobar el límit.

]]> Efectua:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

i, a l'infinit, els límits són equivalents als dels termes de grau més alt

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.5.5.96Q IndetArrel_2 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»an«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</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_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_4</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_5</mi></mtd></mtr><mtr><mtd><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mtd></mtr></mtable><mrow><mi>b_2</mi><mo>≠</mo><mi>b_5</mi></mrow></apply><mrow><mi>a_n</mi><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"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>b_2</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mo>(</mo><mi>c_n</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p13</mi><mo>=</mo><mi>p11</mi><mo>-</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p14</mi><mo>=</mo><msqrt><mrow><mi>b_2</mi><mo>*</mo><mi>n</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p15</mi><mo>=</mo><mi>b_4</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p16</mi><mo>=</mo><mo>-</mo><mo>(</mo><mi>b_4</mi><mo>*</mo><mi>n</mi><msup><mo>)</mo><mn>2</mn></msup></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"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</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"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><mfenced><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>-</mo><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</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> Multiplica i divideix pel conjugat:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»l§#237;m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=f4386473a855d91c5286f2afb57925eb&cw=252&ch=30&cb=18" width="252" height="30" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=f4386473a855d91c5286f2afb57925eb&cw=252&ch=30&cb=18" width="252" height="30" style="vertical-align: -12px;"/>


Simplifica per trobar el límit.

]]> Fes les operacions indicades:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»l§#237;m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»l§#237;m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»l§#237;m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«/mrow»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_n«/mi»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_n«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»l§#237;m«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»16«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»14«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»15«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=38dc0f919889c6ff82b68a2df2ff138f&cw=417&ch=65&cb=31" width="417" height="65" style="vertical-align: -34px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=38dc0f919889c6ff82b68a2df2ff138f&cw=417&ch=65&cb=31" width="417" height="65" style="vertical-align: -34px;"/>

(*) quan eleves «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c_n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=6c4b6c958f95b4ca546e7ebb1eb476cf&cw=42&ch=13&cb=10" width="42" height="13" style="vertical-align: -3px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=6c4b6c958f95b4ca546e7ebb1eb476cf&cw=42&ch=13&cb=10" width="42" height="13" style="vertical-align: -3px;"/> al quadrat no oblidis el doble producte

(**) a l'infinit, ens quedem amb el grau més alt.

Ara ja tens un quocient de polinomis

]]> 1.5.5.97Q IndetNombree Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»


]]>  

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>=</mo><mn>1</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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</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>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>w3</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>=</mo><mi>grau</mi><mo>(</mo><mi>w4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></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"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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"><mi>n</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>20</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</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>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></msup></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"><msup><mroot><exponentiale/><mn>9</mn></mroot><mn>4</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>#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">8</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> La successió és del tipus indeterminació 1∞ i es calcula amb el nombre e:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«msup»«mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»lim«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>

El seu límit és: 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/> = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8734;«/mo»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>

 

]]> 1.5.5.98Q IndetNombree_2 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»


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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi><mo>)</mo><mo>=</mo><mn>1</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"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</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>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>w3</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>=</mo><mi>grau</mi><mo>(</mo><mi>w4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></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"><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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"><mi>n</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>20</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</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>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>9</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mrow><mi>n</mi><mo>+</mo><mn>5</mn></mrow></msup></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"><msup><mroot><exponentiale/><mn>9</mn></mroot><mn>4</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>#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">8</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> La successió és del tipus indeterminació 1∞ i es calcula amb el nombre e:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«msup»«mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»lim«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>

El seu límit és: 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/> = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/>= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8734;«/mo»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>

 

]]> 1.5.5.99Q IndetNombree_3 Calcula el límit de la successió «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»bn«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»cn«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»


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]]> 1.0000000 0.3333333 0 0 #r_81]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b2</mi><mo>≠</mo><mi>b4</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><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>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b4</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>b</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mi>n</mi><mi>p</mi></msup><mo>+</mo><mi>b5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>w3</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>=</mo><mi>grau</mi><mo>(</mo><mi>w4</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>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></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"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</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"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</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>r</mi><mo>_</mo><mn>81</mn></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> La successió és del tipus indeterminació 1∞ i es calcula amb el nombre e:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»lim«/mi»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«msup»«mfenced»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mfenced»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/msup»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»lim«/mi»«mfenced»«mrow»«msub»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msub»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=01923a46befe5ed90e149f3a483be0e0&cw=194&ch=25&cb=20" width="194" height="25" style="vertical-align: -5px;"/>

El seu límit és: 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/>

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=72c6e467332f0597a09597b709fb16d3&cw=129&ch=36&cb=35" width="129" height="36" style="vertical-align: -1px;"/> = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=79094f9d64c84e8bea7eabe510df4501&cw=95&ch=20&cb=19" width="95" height="20" style="vertical-align: -1px;"/> = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mi mathvariant=¨bold¨»l§#237;m«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»w«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=b82d66772334a3aca31a6bd1c9b3f951&cw=69&ch=20&cb=19" width="69" height="20" style="vertical-align: -1px;"/>

Atenció:

  •   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8734;«/mo»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=5aff3d1d26c4c04630b06d74f0f130dd&cw=79&ch=12&cb=11" width="79" height="12" style="vertical-align: -1px;"/>
  •  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=4e27876abc27ae7f96db8e7473c98c99&cw=149&ch=28&cb=16" width="149" height="28" style="vertical-align: -12px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=7061a2b1b7782265b9d66a18712816c9&cw=59&ch=28&cb=24" width="59" height="28" style="vertical-align: -4px;"/>
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mrow»«mroot»«msup»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mo mathvariant=¨bold¨»§#183;«/mo»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mroot»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mroot»«mi mathvariant=¨bold¨»e«/mi»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=75a484ab9b69c926439dd71291058a62&cw=193&ch=42&cb=24" width="193" height="42" style="vertical-align: -18px;"/>

 

 

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