So I was wondering. Let $f:\mathbb{R} \supseteq U \rightarrow \mathbb{R} $ be a function and $p \in \mathbb{R} \cup \left\{ - \infty, +\infty \right\}$ such that
$$\lim_{x \rightarrow p} f(x) = 0$$
Does it now hold that $$\forall a \in \mathbb{R}\setminus \left\{ 0\right\}: \lim_{x \rightarrow p} \frac{a}{f(x)} = \pm \infty$$
That is, the limit $\lim_{x \rightarrow p} \frac{a}{f(x)}$ goes either to infinity or to minus infinity.