JEE Main 2020MathematicsContinuity and DifferentiabilityEasyNumerical

JEE Main 2020 — Continuity and Differentiability Question with Solution

JEE Main 2020 (07 Jan Shift 2)

Question

If the function f defined on -13,1/3 by fx=1xloge1+3x1-2x,when x≠0k,when x=0, is continuous, then k is equal to.

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

limx→0⁡fx=limx→0⁡ln⁡1+3xx-ln⁡1-2xx
=limx→0⁡3ln⁡1+3x3x+2ln1-2x-2x=3+2=5

limfx→0ln1+fxfx=1

∴fx, will be continuous if f0=limx→0⁡fx

Thus, k=5

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About this question

This is a previous-year question from JEE Main 2020, 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.