$ \lim_{x \to \infty} (\frac {x+1}{x+2})^x $ For the limit
$ \lim_{x \to \infty} (\frac {x+1}{x+2})^x $
could you split it up into the fraction $ \lim_{x \to \infty} (1 - \frac{1}{x+2})^x$
and apply the standard limit $ \lim_{x\to+\infty} \left(1+\frac{k}{x}\right)^x=e^k $
or would you have to apply L'Hopitals rule
edit:
oops, forgot to add a term

There's no exponent in your limit.   You can split the fraction up just like you have it,  but then the limit of 1 goes to 1 and the limit of $\frac 1 {x+2}$ goes to 0, so the two limits exist independantly, thus you can subtract the two limits and get the limit is 1.
