## hpfan101 one year ago $\lim_{x \rightarrow \infty} xe^{-x}$

1. hpfan101

$e ^{-x}$

2. anonymous

it is the same as $\lim_{x\to \infty}\frac{x}{e^x}$ does that help?

3. hpfan101

Well, I got that far. And when I take the limit of that, I would get infinity over infinity. Not sure what to do next.

4. anonymous

think what grows faster $$e^x$$ or $$x$$

5. hpfan101

e^x

6. anonymous

of course much much (much) faster

7. hpfan101

So, since the denominator will be a much bigger number, the fraction will be very small. So is the answer of this limit zero?

8. anonymous

yes

9. hpfan101

Ok, thank you! :)