limx→a (a+2x)1/3−(3x)1/3(3a+x)1/3−(4x)1/3,(a≠0) is equal to

limxa(a+2x)1/3(3x)1/3(3a+x)1/3(4x)1/3,(a0) is equal to

  1. A

    29231/3

  2. B

    231/3

  3. C

    294/3

  4. D

    23291/3

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    Solution:

    Let L=limxa(a+2x)1/3(3x)1/3(3a+x)1/3(4x)1/3. Applying L'

    Hospital's rule, we obtain 

    L=limxa23(a+2x)2/3(3x)2/313(3a+x)2/343(4x)2/31 L=13(3a)2/3(4a)2/3 L=13(4a)2/3(3a)2/3=24/335/3=23291/3

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