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Math Help - Evaluating a limit

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    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.
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    Quote Originally Posted by cyber_ninja83 View Post
    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.
    \lim_{h \to 0} \frac{\int_0^h x \cdot f(x) \, dx}{h^2}<br />

    \lim_{h \to 0} \frac{h \cdot f(h)}{2h}<br />

    \lim_{h \to 0} \frac{f(h)}{2} = \frac{f(0)}{2}<br />
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