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JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

\lim_{x\to0}\left(\frac{(x+2\cos x)^3+2(x+2\cos x)^2+3\sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}}

is equal to __________.

Official answer

1

NTA final key (2022 Session 2).

Chapter: Continuity and Differentiability
Topic: L'Hopital's Rule
Idea tested: e-Power Shortcut for 1^infinity Forms

Same idea in other shifts

Asked 2× in all

8 Jan 2020, Shift 1 · Q57 $\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2}$ is equal to :EasySingle correct

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 42 of the 174 JEE Main shifts held from 2017 to 2026.