Solving a Limit: Finding the Right Approach

[twoflower]

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.

 

[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,

 

[twoflower]

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.