1. ## 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?

2. Applying k times L'Hopital's Rule You obtain...

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

Kind regards

$\chi$ $\sigma$