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Math Help - using L'Hopitals Rule

  1. #1
    Super Member bigwave's Avatar
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    Cool 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.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by bigwave View Post
    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}<br />
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