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 a_n = #b_n · #c_n

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

]]> 1.0000000 0.5000000 0 0 #r_81 <question><wirisCasSession><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><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><mi>c_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>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_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><mi>b_5</mi><mo>≠</mo><mi>b_2</mi><mo>∧</mo><mi>b_5</mi><mo>≠</mo><mi>b_3</mi></mrow></apply><mrow><mi>c_5</mi><mo>≠</mo><mi>c_2</mi><mo>∧</mo><mi>c_5</mi><mo>≠</mo><mi>c_3</mi></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><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_5</mi><mo>)</mo></mrow><mrow><mi>b_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><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>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>c_1</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_3</mi><mo>)</mo></mrow><mrow><mi>c_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_5</mi><mo>)</mo></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></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>4</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>6</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>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>42</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>72</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>192</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>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>42</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>72</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>192</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>3</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>42</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>144</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>28</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>3</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>42</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>144</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>28</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>12</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>36</mn></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>32</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>1</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><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 a_n = #b_n : #c_n

]]> 1.0000000 0.5000000 0 0 #r_81 <question><wirisCasSession><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><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><mi>c_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>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_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><mi>b_5</mi><mo>≠</mo><mi>b_2</mi><mo>∧</mo><mi>b_5</mi><mo>≠</mo><mi>b_3</mi></mrow></apply><mrow><mi>c_5</mi><mo>≠</mo><mi>c_2</mi><mo>∧</mo><mi>c_5</mi><mo>≠</mo><mi>c_3</mi></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><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_3</mi><mo>)</mo></mrow><mrow><mi>b_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_5</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>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>c_1</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_3</mi><mo>)</mo></mrow><mrow><mi>c_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_5</mi><mo>)</mo></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><mfrac><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></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></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>3</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>9</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><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>32</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>27</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><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>32</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>27</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>9</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>135</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>486</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>21</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>9</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>135</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>486</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>21</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>7</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>63</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>672</mn></mrow><mrow><mn>27</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>162</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2187</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>13122</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><mfrac><mn>7</mn><mn>27</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #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 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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>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.

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«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:

]]> 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

]]> 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:

El seu límit és:

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:

El seu límit és:

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 a_n = #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.

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»

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»

]]> 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»

]]> 1.0000000 0.5000000 0 0 #r_81 <question><wirisCasSession><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><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><mi>c_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>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_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>c_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><mi>b_5</mi><mo>≠</mo><mi>b_2</mi><mo>∧</mo><mi>b_5</mi><mo>≠</mo><mi>b_3</mi></mrow></apply><mrow><mi>c_5</mi><mo>≠</mo><mi>c_2</mi><mo>∧</mo><mi>c_5</mi><mo>≠</mo><mi>c_3</mi></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><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_3</mi><mo>)</mo></mrow><mrow><mi>b_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>b_5</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>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>c_1</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_2</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_3</mi><mo>)</mo></mrow><mrow><mi>c_4</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>c_5</mi><mo>)</mo></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><mfrac><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></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></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>3</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>9</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><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>32</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>27</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><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>32</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>27</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>9</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>135</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>486</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>21</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>9</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>135</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>486</mn></mrow><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>21</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>7</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>63</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>672</mn></mrow><mrow><mn>27</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>162</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>2187</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>13122</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><mfrac><mn>7</mn><mn>27</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #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 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>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 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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:

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

]]> 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:

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 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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:

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«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»

]]>

]]> 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:

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»«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:

El seu límit és:

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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