(adsbygoogle = window.adsbygoogle || []).push({}); lim(x-->inf) of ((x+a)/(x-a))^x = e

I started this problem and quickly became stuck, the question asks for what value of "a" is the following true:

lim(x-->inf) of ((x+a)/(x-a))^x = e

I took the natural log of both sides to start and got this:

lim(x-->inf) of x*ln((x+a)/(x-a)) = 1

I've tried going on from here but nothing in the end makes sense and i don't know any other way to start the problem; any help is appriciated, thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lim(x->inf) of ((x+a)/(x-a))^x = e

**Physics Forums | Science Articles, Homework Help, Discussion**