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Math Help - difficult limit

  1. #1
    Junior Member
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    difficult limit

    I need help


    \begin{array}{l}<br />
 without\;L'hopital's\;rule\;compute \\ <br />
  \\ <br />
 \lim _{x \to 0} \frac{{x(1 - \cos x)}}{{x - \sin x}} \\ <br />
 \end{array}<br /> <br />
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

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

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

    ... so that...

    Kind regards

    \chi \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; September 4th 2010 at 02:56 PM.
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