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Math Help - L' Hopital's Rule

  1. #1
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    L' Hopital's Rule

    Find the limit \lim_{x\to0^{+}}{ln(sinx)}/{ln(tanx)}
    I'm getting one as my answer but not sure if its right
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  2. #2
    MHF Contributor chisigma's Avatar
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    Once You realize that...

    \ln \tan x = \ln \sin x - \ln \cos x

    ... finding the limit becomes very easy...

    Kind regards

    \chi \sigma
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  3. #3
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    so the answer is +inf
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  4. #4
    MHF Contributor chisigma's Avatar
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    Is...

    \lim_{x \rightarrow 0+} \frac{\ln \sin x}{\ln \tan x}= \lim_{x \rightarrow 0+} \frac{\ln \sin x}{\ln \sin x - \ln \cos x }= \lim_{x \rightarrow 0+} \frac{1}{1+ \frac{\ln \cos x}{\ln \sin x}}

    ... so that...

    Kind regards

    \chi \sigma
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