## Nice limit

Hi all,

could you help me how to solve this limit?

$$\lim_{x \rightarrow \infty} \left( 1 + 10^{-x}\right)^\left(10^x\right)$$

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

 Quote by VietDao29 Hmm,... Look at the problem again, it looks incredibly like: $$\lim_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right) ^ x = e$$ Can you go from here? Viet Dao,
Yep, you're right, can't believe I didn't see it :) Thanks.