JEE Main 2018MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2018 — Continuity and Differentiability Question with Solution

JEE Main 2018 (08 Apr)

Question

Let S=t∈R:fx=x-π ⋅ex-1sinx is not differentiable at t. Then, the set S is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
Bϕ (an empty set)

Step-by-step explanation

fx=x-π.ex-1.sinx

In the neighbourhood of x=π, fx=x-π.ex-1.sinx

Rf′π=limh→0⁡fπ+h-fπh=limh→0hsin⁡π+heπ+h-1h=0

Lf′π=limh→0fπ-fπ-hh=-limh→0-hsin⁡π-heπ-h-1h=0

Differentiable at x=π

Rf′0=limh→0fh-f0h=limh→0h-π×sinheh-1h=0

Lf′0=limh→0⁡f0-f-hh=-limh→0-h-π×sin-he-h-1h=0

Differentiable at x=0

Hence, fx is differentiable everywhere.

⇒S=ϕ

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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.