If f(x) is continuous and differentiable function and f ! ( 1n )=0 for all n 1 and n I then

JEE Advanced Mathematics question

If is continuous and differentiable function and for all and then

Answer: (B)

By continuity at : . Since exists, it can be computed along the sequence :

f'(0)===0.

So (b) holds

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Question ID VK-110180