The value of limx→∞ 2×1/2+3×1/3+4×1/4+…nx1/n(2x−3)1/2+(2x−3)1/3+…+(2x−3)1/n is

The value of limx2x1/2+3x1/3+4x1/4+nx1/n(2x3)1/2+(2x3)1/3++(2x3)1/n is

  1. A

    0

  2. B

    2

  3. C

    2

  4. D

    13

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    Solution:

    Let

    l=limx2x1/2+3x1/3+4x1/4++nx1/n(2x3)1/2+(2x3)1/3++(2x3)1/n

    Then, 

    l=limh02h1/2+3h1/3+4h1/4++nh1/n(23h)1/2h1/2+(23h)1/3h1/3++(23h)1/nh1/n, where h=1x.

     l=limh02+3h1213+4h1214++nh1    12    n(23h)2+(23h)13h1213++(23h)nh121n

     l=22=2

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