If f(x) = where [x] denotes the greatest integer less than…

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If f(x) =

where [x] denotes the greatest integer less than or equal to x, then f(x) equals:

–1

None of these

Text Solution

Verified by Experts

The correct answer is:

As x → 0 – (i.e., approaches 0 from the left), [x] = –1,

∴ f(x) = = –1 + sin 1

whereas, if x → 0 + we get [x] = 0,

∴ f(x) = 0 ⇒ f(x) = 0

Thus, f(x) does not exist.

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