Question

\[\lim_{x \to 0} (1+2x)^x\] I've got \[\lim_{u \to 0} ((1+u)^u)^\frac{1}{2}\]. Is this the only way to do this exercise?

Answer 1

Is the question \[ \lim_{x \to 0} (1+2x)^x\]

Answer 2

Sorry, I update the question. This is the limit that I need to solve, but, I only solve it putting the x equals to 2x. Is this the only way to solve it?

Answer 3

Hmm the question is not updated for me yet, maybe I have to reload the site, give me a second.

Answer 4

ok the question reads for me

\[ \lim_{x \to 0} (1+2x)^x \]
(after reloading the site) and this limit is 1

Answer 5

Aah sorry one more time, I understand that you didn't saw the rest of my question. Yes, this is the limit that I need. You do in the same way that I did?

Answer 6

Did you use a u-substitution? The 2nd equation in your opening post, or was that intended to be the original question?

Answer 7

because what I did to evaluate the limit that I have posted is just plug in x=0, anything to the power ^0 is one, except for 0 (-:

Answer 8

Yes I use u-substitution. It makes sense, you used direct substitution, I didn't think that. Thanks!

Answer 9

in fact it works for both of them, also for the one with the u-substitution.