Let f(x) be defined as follows f(x) = If f(x) is continuou…

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f(x) be defined as follows

f(x) =

If f(x) is continuous at x = 0, then (a, b) =

(e, e)

(e –1 , e –1 )

Text Solution

Verified by Experts

The correct answer is:

We apply check for continuity at x = 0

LHL = f(x) = (0 – h) =

(cos h + sin h) –cosec h (1 ∞ form)

= exp { (cos h + sin h – 1) × – cosec h}

= exp

= exp = e –1

RHL = f(x) = f(0 + h)

∴ For continuity at x = 0,

e –1 = a = b –1 ⇒ a = , b = e.

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