JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 2, Maths Q65

Question 65 of 90 in this shift, Maths question 5 of 30, Section A.

The function

f:\mathbb{R}\to\mathbb{R}

defined by

f(x)=\lim_{n\to\infty}\frac{\cos(2\pi x)-x^{2n}\sin(x-1)}{1+x^{2n+1}-x^{2n}}

is continuous for all

x

in :

(1) $\mathbb{R}-\{-1\}$
(2) $\mathbb{R}-\{-1,1\}$ Official answer
(3) $\mathbb{R}-\{1\}$
(4) $\mathbb{R}-\{0\}$

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Functions Defined by Infinite Limits

Same topic in other shifts

All Continuity and Differentiability questions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.