Let f : [0,∞) → [0,∞) be defined as where [x] is the great…

Maths Definite Integral and Area Under Curves JEE Main 2021 - ( Definite Integration ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Let f : [0,∞) → [0,∞) be defined as

where [x] is the greatest integer less than or equal to x. Which of the following is true?

f is continuous at every point in [0,∞) and differentiable except at the integer points.

f is both continuous and differentiable except at the integer points in [0,∞).

f is continuous everywhere except at the integer points in [0,∞).

f is differentiable at every point in [0,∞). Official

Text Solution

Verified by Experts

The correct answer is:

Let x = n + f, f ∈ (0, 1)

So f(x) = 0 + 1 + 2 +…+ (n − 1) +

Note

so f(x) is cont. ∀ x ≥ 0 and diff. except at integer points

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