Question

Evaluate the Given limit: $\lim_{x\rightarrow -2}$ $\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$

Answer 1

At x = -2, the value of the given function takes the form 0/0.
$\lim_{x\rightarrow -2}$ $\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$=$\lim_{x\rightarrow -2}$ $\frac{\frac{2+x}{2x}}{x+2}$
= $\lim_{x\rightarrow -2}$ $\frac{1}{2x}$
= $\frac{1}{2(-2)}$
= $-\frac{1}{4}$