If limx→a f(x)g(x)  exists, then 

If limxaf(x)g(x)  exists, then 

  1. A

    both limxgf(x) and limx0g(x) must exist 

  2. B

    limxaf(x) need not exist but limxag(x) exists

  3. C

    neither limxaf(x) nor limxag(x) may exist

  4. D

    limxaf(x) exists but limxag(x) need not exist

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    Solution:

    If f(x)=sin1x and g(x)=1x, then both limx0f(x)

    and limx0g(x) do not exist but limx0f(x)g(x)=0 exists.

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