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                     x

Lim           _____   = ?

  

                    x2-1

x→(infinity sign)

Axes24  Mar 4, 2016
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2+0 Answers

 #1
avatar+18712 
+5

                   x

Lim           _____   = ?

  

                    x2-1

x→(infinity sign)

 

\(\begin{array}{rcll} \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& \lim \limits_{x\to \infty} { \left( \dfrac{ x } { x^2-1 } \frac{:x^2}{:x^2} \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2-1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2}{x^2} - \frac{1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{1}{x} } { 1 - \frac{1}{x^2} } \right) } \\ &=& \dfrac{ 0 } { 1 - 0 } \\ &=& \dfrac{ 0 } { 1 } \\ \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& 0 \\ \end{array}\)

 

laugh

heureka  Mar 4, 2016
 #2
avatar+14 
0

Thank you so much!

Axes24  Mar 4, 2016

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