How to use FTC in finding this limit?

**xcluded** · October 28th 2009, 08:30 PM

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

Thanks in advance.

**rn443** · October 28th 2009, 08:54 PM

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 $\lim_{x\to\infty} \frac{e^{e^x}}{e^{e^x}e^x} = \lim_{x\to\infty} e^{-x} = 0$ .

**xcluded** · October 28th 2009, 11:03 PM

Edited.

Thanks !

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