I want to prove that
$$\lim_{x\to \infty}\frac{x^n}{e^x}=0,$$
where $n\in \mathbb{N}$. I already tried to pick some interval as $[0,x]$ or $[x,x+a]$ and let $x$ tend to infinity, but without success...
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Very closely related – Maximilian Janisch Jul 08 '19 at 12:56
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2The OP explictly asks for a proof using the Mean Value Theorem, so I don't think this question is a duplicate. – Mars Plastic Jul 08 '19 at 13:00
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This answer uses l'Hopital's rule, which is a consequence of the Mean Value Theorem. – YuiTo Cheng Jul 08 '19 at 13:38