Function f(x) = [x] cos ; [.] is GIF, is discontinuous at

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

∀ x ∈ R

x ∈ I

x ∉ I

None of these

Text Solution

Verified by Experts

The correct answer is:

At x = n ∈ I LHL. [n – h] cos (2(n–h)–1) π /2

⇒ (n–1)cos(2n–1/2) π =0, RHL.

[n + h]cos(2(n+h)–1/2) π

= n. cos (2n – 1/2) π = 0 f(n) = [n].

cos (2n–1/2) π = 0 so continuous ∀ x ∈ R.

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