# Math Help - using L'Hopitals Rule

1. ## using L'Hopitals Rule

given:

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

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

using L'Hopitals rule

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

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

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

2. Originally Posted by bigwave
given:

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

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

using L'Hopitals rule

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

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

sure there is some very simple way to get this just don't see it off hand.
right ... all you need to do is recognize the form of the limit as a definition of a derivative.

$f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}
$