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Math Help - Sin limit problem

  1. #1
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    Sin limit problem

    I'm having trouble with finding the limit of (sinx)(lnsinx) as x approaches 0 from the positive side. Any suggestions? Thanks!
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  2. #2
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    Why not try L'Hospital's rule?  sin(x) log(sin(x)) = \frac{log(sin(x))}{\frac{1}{sinx}} . That limit has the indeterminate form  \frac{\infty}{\infty} .
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    What he said
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  4. #4
    MHF Contributor chisigma's Avatar
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    For x 'small enough' is \sin x \approx x so that is...

    \lim_{ x \rightarrow 0+} \sin x \cdot \ln \sin x = \lim_{ x \rightarrow 0+} x \cdot \ln x = 0

    Kind regards

    \chi \sigma
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