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Math Help - Does this limit exist?

  1. #1
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    Does this limit exist?

    I'm supposed to calculate the limit if it exists. Can you can firm that this one doesn't exist:

    limit as x approaches 0 of [1 - cos(4x)] / [9x^2]


    I know that

    lim as x approaches 0 of [1 - cos ax] / [ax] = 0, however, I don't think you can manipulate the above to help you.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    \lim_{x\rightarrow 0} \frac{1-cos(4x)}{9x^2}

    = \lim_{x\rightarrow 0} \frac{2sin^2(2x)}{9x^2}

    = \lim_{x\rightarrow 0} \frac{8sin^2(2x)}{9(2x)^2}

    = \frac{8}{9} ( \lim_{x\rightarrow 0} \frac{sinx}{x}=1)
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