Problem 20P

20. If $f$ and $g$ are differentiable functions with $f(0)=g(0)=0$ and $g^{\prime}(0) \neq 0$, show that

$$ \lim _{x \rightarrow 0} \frac{f(x)}{g(x)}=\frac{f^{\prime}(0)}{g^{\prime}(0)} $$

Step-by-Step Solution