Chapter 2 - Limits - Chapter Review Exercises - Page 95: 65

$$A=B$$

Suppose the limits $A, B,$ and $L$ all exist and $L=1 .$ Then \begin{align*} B&=B \cdot 1=B \cdot L\\ &=\lim _{x \rightarrow a} g(x) \cdot \lim _{x \rightarrow a} \frac{f(x)}{g(x)}\\ &=\lim _{x \rightarrow a} g(x) \frac{f(x)}{g(x)}\\ &=\lim _{x \rightarrow a} f(x)\\ &=A \end{align*}