What indeterminant forms do L’Hospital’s Rule apply to?

Question

I am studying L’Hospital’s Rule and I know that it applies to indeterminant forms of the kind:

1. $\frac{0}{0}$
2. $\frac{\pm \infty}{\pm \infty}$

However, what if you have the form say $\frac{0}{\infty}$ or $\frac{\infty}{0}$, does L’Hospital’s Rule still apply?

More formally, if you have $$\lim_{x \rightarrow a} f(x) = \infty \text{ and } \lim_{x \rightarrow b} g(x) = 0,$$ then is it still true that $$\lim_{x \rightarrow a} \frac{f(x)}{g(x)} = \lim_{x \rightarrow a} \frac{f'(x)}{g'(x)}~~?$$

Answer 1

$\frac{0}{\infty} = 0$ and $\frac{\infty}{0} = \infty$. These are not indetermined forms.