# Math Help - limits to infinity

1. ## limits to infinity

how do you find
lim of (1 + 2/x)^x as x tends to infinity?

2. Originally Posted by alexandrabel90
how do you find
lim of (1 + 2/x)^x as x tends to infinity?

If you already know that $\lim_{x\to\infty}\left(1+\frac{1}{f(x)}\right)^{f( x)}=e\,,\mbox { for any function }f(x)\mbox{ s.t. } f(x)\xrightarrow [x\to\infty] {}\infty \mbox{ whenever } x\rightarrow \infty$ ,then:

$\lim_{x\to\infty}\left(1+\frac{2}{x}\right)^x=\lim _{x\to\infty}\left[\left(1+\frac{1}{x\slash 2}\right)^{x\slash2}\right]^2=e^2$

Tonio