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JEE Advanced Mathematics question

MathematicsContinuity and DifferentiabilityJEE Advanced

Let and are finite and definite. Then

Answer: (A),(B)

Solution

The sum of functions differentiable at is differentiable at , with : (b) ✓. Differentiability implies continuity: (a) ✓.

Nothing is known about near . Counter-example for (c) and (d):

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Question ID VK-109346