chain rule " or just simply " continuity ," specifically because $$\lim_{x\to a} f\big(g(x)\big) =f\left(\lim_{x\to a} \,g(x)\right) $$ whenever the limits exist and $f$ is continuous in a neighborhood of $\lim_{x\to a}g(x)$. share | improve this answer edited Feb 18 at 2:30 answered Feb 17 at 22:01 anon 32k 2 41