Question

Evaluate : $\underset{x\to 2}{lim}\frac{x^3-8}{x^2-4}$

Answer 1

We have,

$\underset{x\to 2}{lim}\frac{x^3-8}{x^2-4}$

$=\underset{x\to 2}{lim}\frac{\left(x-2\right)\left(x^2+4+2x\right)}{\left(x-2\right)\left(x+2\right)}$

$=\frac{4+4+4}{4}$

$=\frac{12}{4}$

$=3$

Hence, $3$ is the required answer.