JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q29

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MathematicsInteger+4 / -1Question 29 of 90

$\displaystyle\lim_{x\to0}\left(\frac{(x+2\cos x)^3+2(x+2\cos x)^2+3\sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}x}$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 1

Same first-order terms. The two arguments are $u=x+2\cos x=2+x-x^2+\dots$ and $2+x$ . They differ only at order $x^2$ , so the log of the ratio is $O(x^2)$ .

Limit $e^{0}=1$ .

Answer: 1

Topics:Limits

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JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 29