Posted by **Jenna** on Wednesday, May 20, 2009 at 11:27am.

I am studying for a final exam and in our review packet we have this question, which I am having trouble with:

lim (x-->0) ((e^x)+x)^(1/x)

I tried this problem two ways.

The first was with L'Hopitals rule...

lim(x-->0) (1/x)((e^x)+x)^(1/x-1) * (e^x+1)

but that doesn't seem to help because I don't know what to do with (1/x-1)

Then I tried it like this:

y= ((e^x)+x)^(1/x)

ln y= ln((e^x)+x)^(1/x)

ln y= (1/x)ln((e^x)+x)

and then apply l'hopitals rule (because the above yields 0/0... but I always end up with an x in the denominator.

How do I solve this?

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