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calculus

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solution for limit as delta x approaches 0 (1-cos4x/1-cos2x)

  • calculus - ,

    Usually the first step I take in doing a limit question is to actually substitute the approach value, so I got

    lim cos 4x/(1- cos 2x) , as x -->0
    --> 1/(1-0)
    which is undefined,
    so there is not limit, or the result is infinity

    check: I tried x = .0001
    and got 52631574.74

  • calculus - ,

    however, a more careful reading reveals :-)

    lim (1-cos4x)/(1-cos2x)
    = lim 4sin4x/2sin2x
    = lim (4sin2x cos2x)/sin2x
    = lim 4cos2x
    = 4

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