MATE GGZZ II/5. Gaia-Limiteak eta jarraitasuna Ariketa-10 Kalkulatu funtzio arrazional hauen limiteak:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»)«/mo»«mo»§#160;«/mo»«munder»«mrow»«mi»l«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»1«/mn»«/mrow»«/munder»«mo»§#160;«/mo»«mfenced»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»)«/mo»«mo»§#160;«/mo»«munder»«mrow»«mi»l«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»3«/mn»«/mrow»«/munder»«mo»§#160;«/mo»«mfenced»«mfrac»«mn»3«/mn»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«munder»«mrow»«mi»l«/mi»«mi»i«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»-«/mo»«mn»1«/mn»«/mrow»«/munder»«mo»§#160;«/mo»«mfenced»«mfrac»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«/math»

Idatzi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8709;«/mo»«/math» ez badago limitea.

]]> 1.0000000 0.3333333 0 0 a)Limitea=#l1Alboko limiteak:Eskuinetik=#l1d---------------Ezkerretik=#l1ib)Limitea=#l2Alboko limiteak:Eskuinetik=#l2d---------------Ezkerretik=#l2ic)Limitea=#l3Alboko limiteak:Eskuinetik=#l3d---------------Ezkerretik=#l3i]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1d</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mn>1</mn></mrow></munder><mfenced><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1i</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mn>1</mn></mrow></munder><mfenced><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2d</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mn>3</mn></mrow></munder><mfenced><mfrac><mn>3</mn><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2i</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mn>3</mn></mrow></munder><mfenced><mfrac><mn>3</mn><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3d</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↘</mo><mrow><mo>-</mo><mn>1</mn></mrow></mrow></munder><mfenced><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3i</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>↗</mo><mrow><mo>-</mo><mn>1</mn></mrow></mrow></munder><mfenced><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1d</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>l1i</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>l1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2d</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>l2i</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>l3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3d</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>l3i</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><mi>L</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>A</mi><mi>l</mi><mi>b</mi><mi>o</mi><mi>k</mi><mi>o</mi><mo>&#x000A0;</mo><mi>l</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi>k</mi><mo>:</mo><mi>E</mi><mi>s</mi><mi>k</mi><mi>u</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>1</mn><mi mathvariant="normal">d</mi><mspace linebreak="newline"/><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mi>E</mi><mi>z</mi><mi>k</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>1</mn><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mi>L</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>A</mi><mi>l</mi><mi>b</mi><mi>o</mi><mi>k</mi><mi>o</mi><mo>&#x000A0;</mo><mi>l</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi>k</mi><mo>:</mo><mi>E</mi><mi>s</mi><mi>k</mi><mi>u</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>2</mn><mi mathvariant="normal">d</mi><mspace linebreak="newline"/><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mi>E</mi><mi>z</mi><mi>k</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>2</mn><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mi>L</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>3</mn><mspace linebreak="newline"/><mi>A</mi><mi>l</mi><mi>b</mi><mi>o</mi><mi>k</mi><mi>o</mi><mo>&#x000A0;</mo><mi>l</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi>k</mi><mo>:</mo><mi>E</mi><mi>s</mi><mi>k</mi><mi>u</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>3</mn><mi mathvariant="normal">d</mi><mspace linebreak="newline"/><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mi>E</mi><mi>z</mi><mi>k</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>k</mi><mo>=</mo><mo>#</mo><mi>l</mi><mn>3</mn><mi mathvariant="normal">i</mi></math>]]></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">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>