Nice limit

twoflower

Hi all,

could you help me how to solve this limit?

[tex]
\lim_{x \rightarrow \infty} \left( 1 + 10^{-x}\right)^\left(10^x\right)
[/tex]

Common adjustments for log involving the limit log (1)/0 don't work and no other idea comes to my mind...

Thank you for any help.

VietDao29

Hmm,...
Look at the problem again, it looks incredibly like:
[tex]\lim_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right) ^ x = e[/tex]
Can you go from here?
Viet Dao,

twoflower

Yep, you're right, can't believe I didn't see it :) Thanks.