While I tried to show, that any differentiable function is also steady, I found this lemma but wasn't able to show it. Is it true?
Given two sequences $a_n$ and $b_n$, such that $\lim_{n\to\infty}b_n=0$ and $\lim_{n\to\infty}\frac{a_n}{b_n}$ exist, then $\lim_{n\to\infty}a_n=0.$