JEE Main 2024 — Continuity and Differentiability Question with Solution
JEE Main 2024 (09 Apr Shift 1)
Question
Let be a function given by
where . If is continuous at , then is equal to
where . If is continuous at , then is equal to
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Show full solutionCorrect answer: 81
Correct answer
81
Step-by-step explanation
LHL at
RHL at $\begin{aligned} & \lim _{x \rightarrow \frac{\pi}{2}}(1+|\cot x|)^{\frac{b}{\operatorname{lan}} \tan x} \\ & =e^{\lim _{x-\frac{\pi}{2}}|\cot x| \frac{b}{a}|\tan x|}=e^{\frac{b}{a}} \end{aligned}$
RHL at $\begin{aligned} & \lim _{x \rightarrow \frac{\pi}{2}}(1+|\cot x|)^{\frac{b}{\operatorname{lan}} \tan x} \\ & =e^{\lim _{x-\frac{\pi}{2}}|\cot x| \frac{b}{a}|\tan x|}=e^{\frac{b}{a}} \end{aligned}$
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This is a previous-year question from JEE Main 2024, 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.