Limits: how to find limit [x->infty] of [(x+1/x-1)^x] ?

[takaflaka]

I've been tackling this problem for hours and cannot wrap my head around it. How do I find the limit for (x+1/x-1)^x as x approaches infinity? Can someone please explain each step? I know the answer is e^2 but I understand the process of getting there at all.

 

[ksdhart2]

Well, if you've, as you say, been working on this "for hours," that means you ought to have loads of work to show. If you need a hint to even get started, you might try assuming that limit exists, and it's some real number L. Then you can take the natural log of both sides, leaving a limit that's equal to ln(L). Where does that lead you? Please comply with the rules of the forum as laid out in the Read Before Posting thread that's stickied at the top of every sub-forum and share with us any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.