Question

Evaluate $\underset{x\to -2}{lim}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$.

Answer 1

We have,

$\underset{x\to -2}{lim}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$

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

$=\underset{x\to -2}{lim}\frac{1}{2x}$

$=-\frac{1}{4}.$

Hence, this is the answer.