# Simple L'Hopital Question

I know from definition, that the L'Hopital Rule is the following;

This includes the case $0/0$ and $\dfrac{+-\infty}{+- \infty}$ ... but my question is can LHopital be used on any type of limit like $\dfrac{anything}{\infty}$ ?? this is not mentioned commonly online or in my lecture notes , but is shown in case 2 of the wikipedia article proof;

http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule#General_proof

Any help would be much appreciated

• Yes, it can.${}$ Commented May 30, 2014 at 21:04
• Probably not mentioned in your lecture because it's not easy to replicate (write problems that have $\frac{c}{\infty}$). If Wiki says so, then it's probably right. Commented May 30, 2014 at 21:06

## 1 Answer

Yes, as I mentioned in this answer there is a more general form of the rule, e.g. below from from Rudin's $\:$ Principles of Mathematical Analysis, $\:$ 1976. It requires only that the denominator $\to\infty.\,$ For further such generalizations see the Monthly papers cited here.