The left-hand derivative of f(x) = [x] sin ( π π x) at x = …

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The left-hand derivative of f(x) = [x] sin ( π π x) at x = k, k an integer, is

( − − 1) k (k − − 1) π π

( − − 1) k − − 1 (k − − 1) π π

( − − 1) k k π π

( − − 1) k − − 1 k π π

Text Solution

Verified by Experts

The correct answer is:

(k = integer)

[ ∴ ∴ sin k π π = 0]

= p (k − − 1)( − − 1) k − − 1

∴ ∴ B is the correct alternative.

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