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

 

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfenced><mrow><mi>b_6</mi><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que és el límit d'un polinomi, és igual al límit del seu terme de grau més alt: #g1

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfenced><mrow><mi>b_6</mi><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="intervals">true</param></assertion><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el límit d'un polinomi, per tant és igual al límit del seu monomi de grau més alt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msup»«/mrow»«/mstyle»«/math»

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>b_6</mi><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mi>b_5</mi><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>+</mo><mi>b_4</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b_6</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><ms>-infinit</ms><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el límit d'un polinomi, per tant és igual al límit del seu monomi de grau més alt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msup»«/mrow»«/mstyle»«/math»" src="http://insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=55a9b3688cc15b2816588abb397d423e&cw=57&ch=14&cb=13" width="57" height="14" style="vertical-align: -1px;"/>" 

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

Per determinar el límit d'una fracció algèbrica:

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

 

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mfrac><mi>b_3</mi><mi>b_1</mi></mfrac></mfenced><mo>≠</mo><mfenced close="|" open="|"><mfrac><mi>b_6</mi><mi>b_3</mi></mfrac></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_4</mi></msup></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><ms>-infinit</ms><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És un quocient de polinomis i el grau del numerador és superior. El límit de la successió és igual a: 

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

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mfrac><mi>b_3</mi><mi>b_1</mi></mfrac></mfenced><mo>≠</mo><mfenced close="|" open="|"><mfrac><mi>b_6</mi><mi>b_3</mi></mfrac></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_4</mi></msup></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mi>b_1</mi><mi>b_3</mi></mfrac><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>+∞</cn><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><cn>-∞</cn><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>n</mi><mn>7</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>n</mi><mn>5</mn></msup></mrow><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><ms>-infinit</ms><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És un quocient de polinomis i el grau del numerador és superior. El límit de la successió és igual a: 

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

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mrow><mi>b_2</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el límit d'un quocient de polinomis, i per tant cada polinomi tendeix al límit del seu monomi de grau més alt.

El límit de la successió és: 

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

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mrow><mi>b_2</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>6</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el límit d'un quocient de polinomis, i per tant cada polinomi tendeix al límit del seu monomi de grau més alt.

El límit de la successió és: 

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

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

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que és un quocient de polinomis, fixa't en els termes de grau més alt.

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

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

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

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]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_3</mi><mo>*</mo><mi>n</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><msup><mi>n</mi><mi>b_2</mi></msup><mo>+</mo><mi>b_6</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b_1</mi><mo>/</mo><mi>b_3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>8</mn></msup><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que és un quocient de polinomis, fixa't en els termes de grau més alt.

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

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

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><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>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><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>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>n11</mi><mo>=</mo><mi>n1</mi><mo>*</mo><msup><mi>n</mi><mi>e1</mi></msup><mo>+</mo><mi>n2</mi><mo>*</mo><msup><mi>n</mi><mi>e2</mi></msup><mo>+</mo><mi>n3</mi><mo>*</mo><msup><mi>n</mi><mi>e3</mi></msup></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>d1</mi><mo>*</mo><msup><mi>n</mi><mi>f1</mi></msup><mo>+</mo><mi>d2</mi><mo>*</mo><msup><mi>n</mi><mi>f2</mi></msup><mo>+</mo><mi>d3</mi><mo>*</mo><msup><mi>n</mi><mi>f3</mi></msup></mtd></mtr></mtable><mrow><mi>n1</mi><mo>≠</mo><mi>d1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfrac><mi>n11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>grau</ms><mo> </mo><ms>del</ms><mo> </mo><ms>numerador</ms><mo> </mo><ms>és</ms><mo> </mo><ms>superior</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>límit</ms><mo> </mo><ms>és</ms><mo> </mo><ms>infinit</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> #M1

#M2

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>n</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>n</mi></mrow><mrow><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>grau</ms><mo> </mo><ms>del</ms><mo> </mo><ms>numerador</ms><mo> </mo><ms>és</ms><mo> </mo><ms>superior</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>El</ms><mo> </mo><ms>límit</ms><mo> </mo><ms>és</ms><mo> </mo><ms>infinit</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> #M1

#M2

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>-</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>7</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>9</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>70</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>176</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>90</mn></mrow><mrow><mn>24</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>90</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>81</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_81</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>35</mn><mn>12</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El límit de la diferència és la diferència dels límits

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_3</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>b_5</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>·</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>18</mn></mrow><mrow><mn>12</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>30</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>18</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>6</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El límit del producte és el producte  dels límits

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_1</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mrow><mo>-</mo><mfrac><mi>b_4</mi><mi>b_3</mi></mfrac></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>-</mo><mfrac><mi>b_2</mi><mi>b_5</mi></mfrac></mrow></mfenced><mo>≠</mo><mfenced><mfrac><mi>b_4</mi><mi>b_6</mi></mfrac></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_1</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>b_2</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msqrt><mrow><mi>b_6</mi><mo>*</mo><mi>n</mi><mo>-</mo><mi>b_4</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>a_n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>,</mo><mi>b_4</mi><mo>,</mo><mi>b_5</mi><mo>,</mo><mi>b_6</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>9</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>7</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El límit de la suma  és la suma  dels límits

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

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>e3</mi><mo>=</mo><mi>e1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mi>f1</mi><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>n11</mi><mo>=</mo><mi>n1</mi><mo>*</mo><msup><mi>n</mi><mi>e1</mi></msup><mo>+</mo><mi>n2</mi><mo>*</mo><msup><mi>n</mi><mi>e2</mi></msup><mo>+</mo><mi>n3</mi><mo>*</mo><msup><mi>n</mi><mi>e3</mi></msup></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>d1</mi><mo>*</mo><msup><mi>n</mi><mi>e1</mi></msup><mo>+</mo><mi>d2</mi><mo>*</mo><msup><mi>n</mi><mi>e2</mi></msup><mo>+</mo><mi>d3</mi><mo>*</mo><msup><mi>n</mi><mi>e3</mi></msup></mtd></mtr></mtable><mrow><mi>n1</mi><mo>≠</mo><mi>d1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>c11</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>c12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_n</mi><mo>=</mo><mfrac><mi>n11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>:</mo><mo>=</mo><msup><mfenced><mfrac><mi>n11</mi><mi>d11</mi></mfrac></mfenced><mi>c_n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_n</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mrow><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow><mrow><mn>7</mn><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></mrow></mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>6</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>+∞</cn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El límit de la base de l'exponencial és, ja que es tracta d'un quocient de polinomis de mateix grau: 

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

Només falta elevar-la a l'infinit:

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

 

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