Thread: limit involving exponential

Hello,

I've lurked this forum before but this is my first time posting. I came across a limit this morning that I feel like I really SHOULD be able to answer but can't. I think I'm missing something stupid. Especially since I think this particular limit comes up a bunch.



I've found out that it equals e (from online calculators ) but I have no idea why. I've tried converting it into a rational and using l'Hopital's rule, but I'm getting stuck. Am I on the right track? Any hints?

Originally Posted by erikzb

I've tried converting it into a rational and using l'Hopital's rule, but I'm getting stuck.

Please, post your work.

If we rewrite the limit, this may help.



Now lets take the ln and raise to the e





The limit of

Now we have

Thanks. I definitely was doing something stupid. I changed the function like in your first step, but then took both the top and bottom the the power x, and changed THOSE to exponentials, and tried using L'H. I'm a crazy person.