Limits and Derivatives

Q JEE MAIN 2019

$\lim _{x \rightarrow 1} \frac{\sqrt{\pi}-\sqrt{2 \sin ^{-1} x}}{\sqrt{1-x}}$ is equal to :

JEE Main Mathematics Medium

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Q JEE MAIN 2019

For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim _{x \rightarrow 0^{-}} \frac{x([x]+|x|) \sin [x]}{|x|}$...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

Let $[\mathrm{x}]$ denote the greatest integer less than or equal to x . Then $\lim _{x \rightarrow 0} \frac{\tan \left(\pi \sin ^2 x\right)+(|x|-\sin (x[x]))^2}{x^2}$

JEE Main Mathematics Medium

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Q JEE MAIN 2020

$\lim _{x \rightarrow 0}\left(\frac{3 x^2+2}{7 x^2+2}\right)^{\frac{1}{x^2}}$ is equal to

JEE Main Mathematics Easy

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Q JEE MAIN 2019

If $\lim _{x \rightarrow 1} \frac{x^2-a x+b}{x-1}=5$, then $a+b$ is equal to :

JEE Main Mathematics Easy

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Q JEE MAIN_2021_

If $\lim _{x \rightarrow \infty}\left(\sqrt{x^2-x+1}-a x\right)=b$, then the ordered pair $(a b)$ is :