If f(x) = Where [.] is G.I.F. then -

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

f(x) is differentiable at x = 0

f(x) is differentiable at x = 2

f(x) is continuous but not differentiable at x=0

None of these

Text Solution

Verified by Experts

The correct answer is:

continuity f(2 + ) = 2 + 2 sin (0) = 2

f(2 – ) = 3 + 2 sin (0) = 3 discontinuous at x = 2

at x = 0 f(0 + ) = 2 (0) – 0– 0 × sin (0[0]) = 0

f(0 – ) = 2(0) – (–1) + 0 × sin(0–(–1))

discontinuous at x = 0

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