JEE Main 2018MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2018 — Continuity and Differentiability Question with Solution

JEE Main 2018 (16 Apr Online)

Question

If the function f defined as fx=1x-k-1e2x-1, x≠0 is continuous at x=0, then ordered pair k,f0 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B3,1

Step-by-step explanation

Given fx=1x-k-1e2x-1, x≠0

and fx is continuous at x=0.

⇒f0=limx→01x-k-1e2x-1

=limx→01+2x+12!2x2+…-1-xk-12x2e2x-12x

=limx→01+2x+12!2x2+…-1-xk-12x2

Clearly, k=3 and f0=1. ( ∵Equating coefficient of x=0)

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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.