hpfan101
  • hpfan101
\[\lim_{x \rightarrow \infty} xe^{-x} \]
Calculus1
chestercat
  • chestercat
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hpfan101
  • hpfan101
\[e ^{-x}\]
anonymous
  • anonymous
it is the same as \[\lim_{x\to \infty}\frac{x}{e^x}\] does that help?
hpfan101
  • 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.

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anonymous
  • anonymous
think what grows faster \(e^x\) or \(x\)
hpfan101
  • hpfan101
e^x
anonymous
  • anonymous
of course much much (much) faster
hpfan101
  • 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?
anonymous
  • anonymous
yes
hpfan101
  • hpfan101
Ok, thank you! :)

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