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Math Help - evaluating limits of trig functions #2

  1. #1
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    evaluating limits of trig functions #2

    Can someone check my work for the following and fix accordingly?
    Evaluate the following limits.

    1. lim [1-cos^(2) x]/x^2
    x->0

    2. lim [1-cos2x]/x^2
    x->0

    3. lim cotx/(pi/2 - x)
    x->0

    my work:

    1. lim (sin^(2)x)/x^2
    x->0
    i'm stuck here ..

    2. lim [sin^2 (x) + cos^2 (x) - cos^ 2(x) + sin^2 (x)]/ x^2
    x->0
    = lim [2sin^(2) x]x^2
    x->0
    i'm not sure what step to take next

    3. lim [cos (pi/2 - x)]/ [sin (pi/2 -x)]
    (pi/2 - x) -> 0
    stuck here too..
    Last edited by skeske1234; August 18th 2009 at 01:14 PM.
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  2. #2
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    Quote Originally Posted by skeske1234 View Post

    1. lim (sin^(2)x)/x^2
    x->0
    i'm stuck here ..

    Are you trying to use L'hospitals rule here? If so consider that

    \frac{d}{dx}(1-cos^2x) = sin(2x) and \frac{d}{dx}(x^2) = 2x

    Now have another go at setting up the limit and consider the special case of

    \lim_{x\to 0} \frac{sin(x)}{x}=1
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