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Mathematics 53 Online
OpenStudy (jpsmarinho):

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

OpenStudy (anonymous):

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

OpenStudy (jpsmarinho):

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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (jpsmarinho):

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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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 (-:

OpenStudy (jpsmarinho):

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

OpenStudy (anonymous):

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

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