The value of limx→0 1−cos⁡(1−cos⁡x))x4, is

The value of limx01cos(1cosx))x4, is

  1. A

    18

  2. B

    12

  3. C

    14

  4. D

    none of these

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    Solution:

    We have, 

    limx01cos(1cosx)x4=limx01cos2sin2x/2x4=limx02sin2sin2x/2x4=2limx0sinsin2x/2x22=2limx0sinsin2x/2sin2x/2×sin2x/2x2/4×142=2142=18 ALITER limx01cos(1cosx)x4=limx01cos(1cosx)(1cosx)21cosxx22=12×122=18

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