For a real number x, let [x] denote the greatest integer le…

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

For a real number x, let [x] denote the greatest integer less than or equal to x-

Then f(x) = is-

Continuous at some x

Continuous at all x but f '(x) does not exist for some x

f '(x) exists for all x but f '' (x) does not exist

f ' (x) exists for all x

Text Solution

Verified by Experts

The correct answer is:

 [x – π ] = Integer

∴ tan π [x – π ] = 0

∴ = 0 → Constant fn ⇒ always continuous and differentiable

⇒ f (x) , f ' (x) , f " (x) ..... = 0 ∀ x ∈ R

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.