Question

Evaluate the following limit:
$\underset{x\to -2}{\text{lim}}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$

Answer 1

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

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

=$\underset{x\to -2}{\text{lim}}\frac{1}{2x}=\frac{1}{2\times -2}=\frac{-1}{4}$.