JEE Main 2024MathematicsLimitsEasyMCQ

JEE Main 2024 — Limits Question with Solution

JEE Main 2024 (31 Jan Shift 2)

Question

Let f:→R→0,∞ be strictly increasing function such that limx→∞f7xfx=1. Then, the value of limx→∞f5xfx−1 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B0

Step-by-step explanation

Let, x be any poistive real number.

⇒x<5x<7x

⇒fx<f5x<f7x

⇒fxfx<f5xfx<f7xfx

⇒1<f5xfx<f7xfx

⇒limx→∞1<limx→∞f5xfx<limx→∞f7xfx

It is given that, limx→∞f7xfx=1

So, by using Sandwich theorem,

⇒limx→∞f5xfx=1

⇒limx→∞f5xfx-1=0

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About this question

This is a previous-year question from JEE Main 2024, 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.