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Question

If limx0 (1+ax)bx=e4 where a and b are natural numbers, then 
  1. ab=8
  2. a=8, b=4
  3. ab=4
  4. a=4, b=8


Solution

The correct option is C ab=4
limx0 (1+ax)bx   1 form
limx0 b(1+ax)x=4loge
limx0 b+abxx=4
Apply L'Hospital
ab=4

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