Let L=limx→0 a−a2−x2−x2/4×4,a>0 If L is finite, then

Let L=limx0aa2x2x2/4x4,a>0 If L is finite, then

  1. A

    a=2,L=164

  2. B

    a=1,L=164

  3. C

    a=3,L=132

  4. D

    a=1,L=132

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    Solution:

    We have,

    L=limx0aa2x2x24x4 L=limx0a-a2x2x24x4 L=limx01x21a+a2x214

     L=limx04aa2x24x2a+a2x2

    It is given that L is finite.

    limx04aa2x204aa=0a=2

    Putting a=2, we obtain

    L=limx024x24x22+4x2L=limx044x24x22+4x22L=limx0142+4x22=164

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