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QJEE-MAIN 2020
$\lim _{x \rightarrow a} \frac{(a+2 x)^{\frac{1}{3}}-(3 x)^{\frac{1}{3}}}{(3 a+x)^{\frac{1}{3}}-(4 x)^{\frac{1}{3}}}(a \neq 0)$ is equal to :
$(3 a+x)^{\frac{1}{3}}-(4 x)^{\frac{1}{3}}$
JEE MainMathematicsEasy
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QJEE MAIN 2019
$\lim _{x \rightarrow 0} \frac{x \cot (4 x)}{\sin ^2 x \cot ^2(2 x)}$ is equal to
JEE MainMathematicsEasy
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QJEE MAIN 2020
$\lim _{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ is equal to $\_\_\_\_$ .
JEE MainMathematicsMedium
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QJEE MAIN 2019
If $f(x)=[x]-\left[\frac{x}{4}\right], x \in R$, where $[x]$ denotes the greatest integer function, then :
JEE MainMathematicsEasy
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QJEE MAIN 2021
$\lim _{x \rightarrow 0} \frac{\sin ^2\left(\pi \cos ^4 x\right)}{x^4}$ is equal to:
JEE MainMathematicsMedium
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QJEE Main 2021
If $\alpha=\lim _{x \rightarrow \pi / 4} \frac{\tan ^3 x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}$ and $\beta=\lim _{x \rightarrow 0}(\cos x)^{\cot x}$ are the roots of the equation,...
JEE MainMathematicsMedium
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QJEE MAIN 2021
If $\alpha, \beta$ are the distinct roots of $x^2+b x+c=0$, then $\lim _{x \rightarrow \beta} \frac{e^{2\left(x^2+b x+c\right)}-1-2\left(x^2+b x+c\right)}{(x-\beta)^2}$ is equal to :
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