# Thread:

1. ## How to use FTC in finding this limit?

$\lim_{x\,\to\,\infty}e^{-e^{x}}\int_0^x e^{e^{t}}dt$

Thanks in advance.

2. Originally Posted by xcluded
$\lim_{x\,\to\,\infty}e^{-e^{x}}\int_0^x e^{e^{t}}dt$

Thanks in advance.
Express the limit as $\lim_{x\to\infty} \frac{\int_0^x e^{e^t}dt}{e^{e^x}}$. Both the numerator and denominator approach infinity, so by L'Hopital's rule and the fundamental theorem of calculus, the limit equals $\lim_{x\to\infty} \frac{e^{e^x}}{e^{e^x}e^x} = \lim_{x\to\infty} e^{-x} = 0$.

3. Edited.

Thanks !
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