Limit question

1. Feb 28, 2010

talolard

1. The problem statement, all variables and given/known data
I've done thsi limit, i think I'm half right. I'm sure I have done something wrong, but I'm not sure what.

$$lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^(x/lnx)$$

3. The attempt at a solution
$$lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^{x/lnx} = lim_{x-> \infty} ( \frac {x(1 +\frac {lnx}{x})}{x(1- \frac {lnx}{x})})^{x/lnx}=$$
$$t= \frac {x}{lnx}; lim_{t-> \infty} (\frac {1 + \frac {1}{t}} {1 - \frac{1}{t}})^t=$$
$$\frac {e}{e^{-1}}=e^2$$

Last edited: Feb 28, 2010
2. Feb 28, 2010

vela

Staff Emeritus
That's right.