f(x) = (sin -1 x)². cos (1/x) if x ≠ 0; f(0) = 0, f(x) is:

Maths Functions, Limits, Continuity and Differentiability General More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

continuous no where in − 1 ≤ x ≤ 1

continuous everywhere in − 1 ≤ x ≤ 1

differentiable no where in − 1 ≤ x ≤ 1

differentiable everywhere in − 1 < x < 1

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b,d)

f(x) can be discontinuous only at x = 0 in [–1,1]

So we check only at x = 0

LHD (x = 0) =

= –1. 0. [finite quantity between [–1,1]] = 0

RHD (x = 0) is

Hence f(x) is differentiable as well as continuous in [–1,1]

──────────────────────────────────────────────────────────────────────────────────────────

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.