JEE Main 2021MathematicsContinuity and DifferentiabilityEasyNumerical

JEE Main 2021 — Continuity and Differentiability Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

Let f : R→R satisfy the equation f(x+y)=f(x)·f(y) for all x,y∈R and f(x)≠0 for any x∈R. If the function f is differentiable at x=0 and f'(0)=3, then limh→01hfh-1 is equal to ___ .

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

If f(x+y)=f(x)·f(y) & f'(0)=3 then

f(x)=ax⇒f'x=ax·lna

⇒f'0=lna=3⇒a=e3

⇒fx=e3x=e3x

limx→0f(x)-1x=limx→0e3x-13x×3=1×3=3

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About this question

This is a previous-year question from JEE Main 2021, 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.