given:

$\displaystyle \lim_{h \to 0}\frac{\ln{(e+h)}-1}{h}$

since this has the inderterminate form of $\displaystyle \frac{0}{0}$

using L'Hopitals rule

I would presume the limit can be found as $\displaystyle f'(e)$ where $\displaystyle f(x)=\ln{x}$

the answer is $\displaystyle \frac{1}{e}$

sure there is some very simple way to get this just don't see it off hand.