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Limits and Derivatives

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN_2021_
The value of
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Q JEE MAIN 2021
$\lim _{n \rightarrow \infty} \tan \left\{\sum_{r=1}^n \tan ^{-1}\left(\frac{1}{1+r+r^2}\right)\right\}$ is equal to $\_\_\_\_$ .
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Q JEE MAIN 2021
If $\lim _{x \rightarrow 0} \frac{\sin ^{-1} x-\tan ^{-1} x}{3 x^2}$ is equal to $L$, then the value of $(6 L+1)$ is
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Q JEE-MAIN 2021
If $\lim _{x \rightarrow 0} \frac{a e^x-b \cos x+c e^{-x}}{x \sin x}=2$, then $a+b+c$ is equal to $\_\_\_\_$ .
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Q JEE MAIN 2021
Let $S_k=\sum_{r=1}^k \tan ^{-1}\left(\frac{6^r}{2^{2 r+1}+3^{2 r+1}}\right)$. Then $\lim _{k \rightarrow \infty} S_k$ is equal to :
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Q JEE MAIN 2021
Let $f(x)=\sin ^{-1} x$ and $g(x)=\frac{x^2-x-2}{2 x^2-x-6}$. If $g(2)=\lim _{x \rightarrow 2} g(x)$, then the domain of the function fog is :
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Q JEE MAIN 2021
The value of $\lim _{h \rightarrow 0} 2\left\{\frac{\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)+\cos \left(\frac{\pi}{6}+h\right)}{\sqrt{3} h(\sqrt{3} \cos h-\sin h)}\right\}$ is
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Q JEE MAIN 2021
$\lim _{n \rightarrow \infty}\left(1+\frac{1+\frac{1}{2}+\ldots \ldots+\frac{1}{n}}{n^2}\right)^n$ is equal to :
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Q JEE MAIN 2022
If $\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0$ then $8(\alpha+\beta)$ is equal to :
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Q JEE MAIN 2022
Let $[t]$ denote the greatest integer $\leq t$ and $\{t\}$ denote the fractional part of $t$. Then integral value of $\alpha$ for which the left...
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