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Most Important Selected Qs for JEE AdvancedMathematicsLimits

Let f:[0,1] R be a differentiable function with f(0)=0 , then _ n n^2 ₀^ 1 / n f(t) d t equals

Options

  1. A1 2 f ^ (0)
  2. Bf^ (0)
  3. C2 f ^ (0)
  4. D0

Correct answer

A. 1 2 f ^ (0)

Step-by-step solution

I= _ n ₀^ 1 / n f(t) d t 1 n^2 ( 0 0 form ) Using : L' Hospital and using Leibnitz rule I= _ n n^3 f ( 1 n ) (- 1 n^2 ) -2 = _ n n 2 f ( 1 n ) Put n = 1 ~h hence I= 1 2 _ h 0 ( f(0+h)-f(0) h )= 1 2 f^ (0)

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