# Limits Problem

• March 1st 2010, 08:39 AM
craig
Limits Problem
Show that for any k, $\lim_{x\to\infty}\frac{x^{k}}{e^{x}}\to0$.

I'm thinking that this has something to do with l'Hopital's Rule, showing that $x^{k} > e^{x}$, not sure where to start though?

$\lim_{x \rightarrow \infty} \frac{x^{k}}{e^{x}} = \lim_{x \rightarrow \infty} \frac{k!}{e^{x}} = 0$
$\chi$ $\sigma$