I am presented with the following task:
"You are given that $k(h) \neq 0$ and $h \neq 0$. If $\lim_{k \to 0} F(k) = L$ and $\lim_{h \to 0} k(h) = 0$, show that $\lim_{h \to 0}F(k(h)) = L$.
This is the first part of a task that the professor marked with "Hard and theoretical", so I assume that it gets more complicated as we go, but I am wondering if my logic here is correct:
Given that $\lim_{h \to 0} k(h) = 0$, using $k(h)$ as the "inner part" (if there's a better word for this, let me know) of a composite function makes no difference for the result, thus $\lim_{h \to 0}F(k(h)) = L$. This is under the prerequisite that $k(h) \neq 0$, which we are already given.