limx→2 (x^3−8)/(12x−24)

$\lim \limits_{x\to 2} { \frac{x^3-8}{12x-24} }$

l'Hospital's rule

$\begin{array}{rcll} \lim \limits_{x\to 2} { \frac{x^3-8}{12x-24} } &=& \lim \limits_{x\to 2} { \frac{3x^2}{12} }\\ &=& { \frac{3\cdot 2^2}{12} }\\ &=& { \frac{12}{12} }\\ \mathbf{\lim \limits_{x\to 2} { \frac{x^3-8}{12x-24} } }&\mathbf{=}& \mathbf{1}\\ \end{array}$