JEE Main 2016 Mathematics question
If is a differentiable function in the interval such that and , for each , then is equal to
Answer: (4)
Solution
The limit is of the form as , so apply L'Hôpital's rule differentiating with respect to :
= 2x f(x) - '(x) = 1.
Rearranged, this is the linear differential equation . Dividing by makes the left side an exact derivative:
\
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