1. ## Evaluating a limit

We just learned l'Hopital's rule in class and I am having a difficult time evaluating a limit with it. The question provides the limit as h approaches zero of (1/h^2) * integral of x*f(x)dx from 0 to h. Any help is greatly appreciated. I am trying to use integration by parts first and then apply l'Hopital's rule, but when I check with some test values, my answers are always wrong.

2. Originally Posted by cyber_ninja83
We just learned l'Hopital's rule in class and I am having a difficult time evaluating a limit with it. The question provides the limit as h approaches zero of (1/h^2) * integral of x*f(x)dx from 0 to h. Any help is greatly appreciated. I am trying to use integration by parts first and then apply l'Hopital's rule, but when I check with some test values, my answers are always wrong.
$\displaystyle \lim_{h \to 0} \frac{\int_0^h x \cdot f(x) \, dx}{h^2}$

$\displaystyle \lim_{h \to 0} \frac{h \cdot f(h)}{2h}$

$\displaystyle \lim_{h \to 0} \frac{f(h)}{2} = \frac{f(0)}{2}$