How would I prove that

$\displaystyle \lim\limits_{x\to\infty}xe^{-x}=0$ ?

I've only done eps-delta proofs for finite limit points, not to infinity.

Printable View

- Jun 27th 2010, 03:57 AMscorpion007Fairly simple limit proof?
How would I prove that

$\displaystyle \lim\limits_{x\to\infty}xe^{-x}=0$ ?

I've only done eps-delta proofs for finite limit points, not to infinity. - Jun 27th 2010, 04:18 AMDeadstar
Are you familiar with L'Hopitals rule?

- Jun 27th 2010, 04:29 AMscorpion007
Yes. I think I may know how to solve it then. -- Wait, but LHopitals rule is for finding the limit, not proving it?

- Jun 27th 2010, 05:20 AMmr fantastic
- Jun 27th 2010, 04:18 PMscorpion007
It arose indirectly from me solving an integral of the form $\displaystyle \int_0^\infty xe^{-x} $ where I had to evaluate the limit of a similar expression, and was curious if I could prove it using a method like e-d proofs.

- Jun 27th 2010, 05:09 PMPlato
- Jun 27th 2010, 05:19 PMscorpion007
Only because I was curious if I could prove it -- not because it was strictly necessary to do so.

- Jun 27th 2010, 05:28 PMAlso sprach Zarathustra