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Math Help - finding a limit with trig

  1. #1
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    finding a limit with trig

    Question

    find the limit or prove it does not exist

    limx->0 xsinx/1-cosx

    just pluging this into my calculator it looks like the limit is 2 but i can't figure out how to get this... i should mention it looks like there is no slope there, i know that means that there is no derivative there but i forgot if that also means the limit is undefined?

    thanks
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  2. #2
    MHF Contributor
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    Beginning with \frac{x \sin x}{1 - \cos x}, multiply by \frac{1 + \cos x}{1 + \cos x} to obtain:

    \frac{x (\sin x)(1 + \cos x)}{1 - \cos^2 x}

    \frac{x (\sin x)(1 + \cos x)}{\sin^2 x}

    \frac{x(1 + \cos x)}{\sin x}

    \frac{x}{\sin x} \cdot {(1 + \cos x)}

    The limit on the left is 1, and the limit on the right is 2. Hence the limit of the product is 2.
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  3. #3
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    awesome thank you very much
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