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Math Help - Limits of trig functions

  1. #1
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    Limits of trig functions

    Can someone help me with the following questions:

    1) [1-cos2x]/[x^2] as x approaches 0
    2) [cotx]/[pi/2 - x] as x approaches pi/2
    3) [sin]/[x-pi] as x approaches pi

    I know that 1-cosx/x^2 is 1/2, but I don't know how this could be used when it's cos2x. I'm not really sure how I could approach the second or third questions. Could I get some advice?
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  2. #2
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    Try some trig identities

    \lim_{x \to 0}\frac{1-\cos(2x)}{x^2}=\lim_{x \to 0}\frac{2\sin^{2}(x)}{x^2}=2
    Last edited by TheEmptySet; March 30th 2008 at 05:03 PM. Reason: Wrong trig
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by theowne View Post
    Can someone help me with the following questions:

    1) [1-cos2x]/[x^2] as x approaches 0
    2) [cotx]/[pi/2 - x] as x approaches pi/2
    3) [sin]/[x-pi] as x approaches pi

    I know that 1-cosx/x^2 is 1/2, but I don't know how this could be used when it's cos2x. I'm not really sure how I could approach the second or third questions. Could I get some advice?
    for 3 let u=x - \pi

    \lim_{x \to \pi}\frac{\sin(x)}{x-\pi}=\lim_{u \to 0}\frac{\sin(u + \pi)}{u}

    Now use the sum identity for sine

    Try the same thing on #2.

    Good luck.
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