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Limits and Derivatives

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
$\lim _{x \rightarrow 2}\left(\sum_{n=1}^9 \frac{x}{n(n+1) x^2+2(2 n+1) x+4}\right)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $f(x)=x^6+2 x^4+x^3+2 x+3, x \in R$. Then the natural number $n$ for which $\lim _{x \rightarrow 1} \frac{x^n f(1)-f(x)}{x-1}=44$ is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021 S2
The value of $\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}}\right)$ is equal to:
JEE Main Mathematics Medium
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Q JEE MAIN 2019
Let $f: R \rightarrow R$ be a differentiable function satifying $f^{\prime}(3)+f^{\prime}(2)=0$. Then $\lim _{x \rightarrow 0}\left(\frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)}\right)^{\frac{1}{x}}$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f: R \rightarrow R$ be a function such that $f(2)=4$ and $f(2)=1$. Then, the value of $\lim _{x \rightarrow 2} \frac{x^2 f(2)-4 f(x)}{x-2}$ is...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If the value of $\lim _{x \rightarrow 0}(2-\cos x \sqrt{\cos 2 x})^{\left(\frac{x+2}{x^2}\right)}$ is equal to $e^a$, then a is equal to $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If $\lim _{x \rightarrow 0} \frac{a x-\left(e^{4 x}-1\right)}{a x\left(e^{4 x}-1\right)}$ exists and is equal to $b$, then the value of $a-2 b$ is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If $\lim _{x \rightarrow 0} \frac{\alpha x e^x-\beta \log _e(1+x)+\gamma x^2 e^{-x}}{x \sin ^2 x}=10, \alpha, \beta, \gamma \in R$, then the value of $\alpha+\beta+\gamma$...
JEE Main Mathematics Medium
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Q JEE-MAIN 2021
The value of the limit $\lim _{\theta \rightarrow 0} \frac{\tan \left(\pi \cos ^2 \theta\right)}{\left(2 \pi \sin ^2 \theta\right)}$ equal to:
JEE Main Mathematics Easy
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Q JEE-MAIN 2021
The value of $\lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots \ldots+[n r]}{n^2}$ where $r$ is non-zero real number and $[r]$ denotes the greatest integer less than...
JEE Main Mathematics Easy
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