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Math Help - Introductory Calculus Question (trig limit)

  1. #1
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    Introductory Calculus Question (trig limit)

    limit as x approaches zero of (1-cos^4(x ))/(sin2x)^2 = ??

    I can get to
    (1-cos^4(x ))/(sin2x)^2 = (1-cos^2x)(1+cos^2x) / ((2sinxcosx)(2sinxcosx))
    the denominator might be wrong sin2x=2sinxcosx .

    Or alternatively,

    (1-cos^4(x ))/(sin2x)^2 = (1+cos^2(x ))(sin^2(x ))/sin^2 (2x)

    Thanks for looking. I can't get it past there. The idea is to get to a point where things can be simplified by the following:

    the lim as x approaches zero of sinx/x = 1
    the lim as x approaches zero of sinx=0
    the lim as x approaches zero of cosx=1
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  2. #2
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    Angry

    Thank you in advance, if you're up for it, there are a couple more I'm stuck on. This one just really bothers me because I put a couple pages and about an hour of thinking into it
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  3. #3
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    Re:

    Some problem for your first time...
    Attached Thumbnails Attached Thumbnails Introductory Calculus Question (trig limit)-limit.gif  
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  4. #4
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    that's ridiculously more straightforward than I was expecting.
    All the textbook question in this chapter for solving limits have been of the following format (no differentiating, just rearanging):

    Find the limit as x approaches zero of (sin^2xcosx)/(1-cosx)

    = lim as x approaches zero of (sin^2xcosx(1+cosx))/(1-cos^2x)
    = lim as x approaches zero of (cosx(1+cosx))
    =1(1+1)
    =2

    The rest of my limit questions make a lot more sense with a differential approach :P THanks again!
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  5. #5
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    Re:

    do you need this one work out too?


    -qbkr21
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  6. #6
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    I think my solution is correct. I'll make another thread in the calculus forum with some other questions.
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