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Thread: difficult limit

  1. #1
    Junior Member
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    difficult limit

    I need help


    $\displaystyle \begin{array}{l}
    without\;L'hopital's\;rule\;compute \\
    \\
    \lim _{x \to 0} \frac{{x(1 - \cos x)}}{{x - \sin x}} \\
    \end{array}

    $
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

    $\displaystyle \displaystyle x\ (1-\cos x) = \frac{x^{3}}{2} - \frac{x^{5}}{24} + ...$

    $\displaystyle \displaystyle x - \sin x = \frac{x^{3}}{6} - \frac{x^{5}}{120} + ... $

    ... so that...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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  3. #3
    Senior Member
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    deleted since it would still require l'Hospital.
    Last edited by lvleph; Sep 4th 2010 at 02:56 PM.
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