# Evaluate the following limits: $\lim\limits_{x \to -2} \Large\frac{ \Large\frac{1}{x}+ \Large\frac{1}{2}}{ \normalsize x +2}$

$\begin{array}{1 1} \frac{-1}{4} \\ \frac{-1}{2} \\ \frac{1}{4} \\ \frac{1}{2} \end{array}$

$\lim\limits_{x \to -2} \large\frac{ \Large\frac{1}{x}+ \Large\frac{1}{2}}{ x +2}$
At $x = -2$ the value of the given function takes the form $\large\frac{0}{0}.$
Now, $\lim\limits_{x \to -2} \large\frac{ \Large\frac{1}{x}+ \Large\frac{1}{2}}{ x +2}$ $= \lim\limits_{x \to -2} \large\frac{\bigg( \Large\frac{2+x}{2x} \bigg) }{x+2}$
$= \lim\limits_{x \to -2} \large\frac{ 1}{2x}$