For this question, should I use differentiation method or the integration method ?
$\lim_{x\to \infty} (\frac{x}{x+2})^{x/8}$
this is what i got so far:
Note: $\lim \limits_{n\to\infty} [1 + (a/n)]^n = e^{\underline{a}}\ldots\ldots (1)$
$ L = \lim \left[\frac{x}{x+2}\right]^{x/8} = \lim\left[\frac{1}{\frac{x+2}{x}}\right]^{x/8} =\frac{1}{\lim [1 + (2/x)]^x]^{1/8}} $
but i'm not sure where to go from there