JEE Main 2023MathematicsLimitsHardMCQ

JEE Main 2023 — Limits Question with Solution

JEE Main 2023 (30 Jan Shift 2)

Question

Let f,g and h be the real valued functions defined on ℝ as fx=xx,x≠01,x=0,   gx=sinx+1x+1,x≠-11,x=-1and hx=2x-fx, where x is the greatest integer ≤x. Then the value of limx→1ghx-1 is

Choose an option

Show full solutionCorrect option: A
Correct answer
A1

Step-by-step explanation

Given,

Function fx=xx,x≠01,x=0,   gx=sinx+1x+1,x≠-11,x=-1 and hx=2x-fx

To find limx→1ghx-1

Taking L.H.L, we take x=1-h

limh→0-g(h(1-h-1))

⇒limh→0-g2-h--h-h

⇒limh→0-g(2(-1)+1)

⇒limh→0-g-1=1

Now taking R.H.L, we take x=1+h

limh→0+g(h(1+h-1))

=limh→0+g2h-f(h)

=limh→0+g(0-1)

⇒limh→0+1=1

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Limits chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, covering the Limits 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.