Question

Evaluate the following limit:
$\underset{x\to 2}{\text{lim}}\frac{3x^2-x-10}{x^2-4}$

Answer 1

$\underset{x\to 2}{\text{lim}}\frac{3x^2-x-10}{x^2-4}\left[\frac{0}{0}\text{form}\right]$

= $\underset{x\to 2}{\text{lim}}\frac{(x-2)(3x+5)}{(x-2)(x-2)}$

= $\underset{x\to 2}{\text{lim}}\frac{3x+5}{x+2}=\frac{6+5}{2+2}=\frac{11}{4}$