+26367 x
Lim _____ = ?
x2-1
x→(infinity sign)
\(\begin{array}{rcll} \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& \lim \limits_{x\to \infty} { \left( \dfrac{ x } { x^2-1 } \frac{:x^2}{:x^2} \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2-1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{x}{x^2} } { \frac{x^2}{x^2} - \frac{1}{x^2} } \right) } \\ &=& \lim \limits_{x\to \infty} { \left( \dfrac{ \frac{1}{x} } { 1 - \frac{1}{x^2} } \right) } \\ &=& \dfrac{ 0 } { 1 - 0 } \\ &=& \dfrac{ 0 } { 1 } \\ \lim \limits_{x\to \infty} { \left( \dfrac{x } { x^2-1 } \right) } &=& 0 \\ \end{array}\)
