JEE Main 2018MathematicsContinuity and DifferentiabilityHardMCQ

JEE Main 2018 — Continuity and Differentiability Question with Solution

JEE Main 2018 (15 Apr)

Question

Let S={λ, μ∈R×R : ft=λ et-μsin⁡2t, t∈R is a differential function}. Then, S is a subset of :

Choose an option

Show full solutionCorrect option: B
Correct answer
BR×0, ∞)

Step-by-step explanation

Let S=λ, μ∈R×R and

ft=λet-μ. sin⁡2t

RHD=limh→0⁡f0+h-0h=limh→0⁡λeh-μsin2⁡hh=2(λ-μ)

LHD=limh→0⁡f0-h-0-h=limh→0⁡λeh-μsin2⁡h-h=-2(λ-μ)

Now, LHD=RHD if λ=μ

⇒μ≥0 and λ∈R

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About this question

This is a previous-year question from JEE Main 2018, covering the Continuity and Differentiability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.