Chain Rule - Supporting Problem 2
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Problem:
Prove that if
- $g(x)$ is differentiable at $a$
- $f(x)$ is differentiable at $g(a)$
- for all $\bar{\delta}\gt0$ there exists an $x$ in the interval $(a-\bar{\delta},a)\cup(a,a+\delta)$ such that $g(x)=g(a)$
are true then
\[
\lim_{x\to a}\frac{f(g(x))-f(g(a))}{x-a}=0.
\]
Answer:
