Question

\[\lim_{x \rightarrow \infty} xe^{-x} \]

Answer 1

\[e ^{-x}\]

Answer 2

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

Answer 3

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.

Answer 4

think
what grows faster \(e^x\) or \(x\)

Answer 5

e^x

Answer 6

of course
much much (much) faster

Answer 7

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

Answer 8

yes

Answer 9

Ok, thank you! :)