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Math Help - Trig Limits

  1. #1
    Senior Member
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    Exclamation Trig Limits

    Hi

    How do I work out:

    lim x --> 0 [(cos2x - 1)/x]

    Is it 0?

    Thanx
    Last edited by xwrathbringerx; August 12th 2009 at 07:12 AM.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \lim_{x\to 0}\frac{\cos 2x-1}{x}=\lim_{x\to 0}\frac{1-2\sin^2x-1}{x}=\lim_{x\to 0}\frac{-2\sin^2x}{x}=

    =-2\lim_{x\to 0}\frac{\sin x}{x}\sin x=-2\cdot 1\cdot 0=0
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