Chapter 1.2, Problem 52ES

Suppose that $f$ and $g$ are two functions such that $\underset{x\to a}{\lim }g\left(x\right)=0\text{ and }\underset{x\to a}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$ exists. Use Theorem $\mathrm{1.2.2}$ to prove that ${\lim }_{x\to a}f\left(x\right)=0$ .