TITLE: L’Hopital’s rule for (infinity over minus infinity)
QUESTION [6 upvotes]: Can I apply L’Hopital’s rule to this:
$$
\lim_{x\to0}\frac{f(x)}{g(x)} 
$$
when $
\lim_{x\to0}f(x) = \infty
$ and $
\lim_{x\to0}g(x) = -\infty
$. Is this an indeterminate form?

REPLY [7 votes]: Yes.
$\lim_{x\to0}\dfrac{f(x)}{g(x)}$ in which $\lim_{x\to0}f(x) = \infty,$ and $\lim_{x\to0}g(x) = -\infty$ (or vice versa)
or informally,  $\lim_{x\to 0}\dfrac {f(x)}{g(x)} \to  \dfrac \infty{-\infty} $, and/or such a limit that approaches $\frac {-\infty}\infty$
are indeterminate forms. 
A handy list of the other indeterminate forms is given by Wikepedia. The entry itself is rather useful.
You can use  l’Hospital’s rule in such each case above.