1rBTX 05. SUCCESSIONS/1.5.5 Resolució d'indeterminacions 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:

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i simplificar per trobar el límit.

]]> Efectua:

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

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