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Continuity and Differentiability

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE Main 2019
Let $f: R \rightarrow R$ be a function defined as $$ f(x)=\left\{\begin{array}{rrr} 5, & \text { if } & x \leq 1 \\ a+b x,...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x-[x], g(x)=1-x+[x]$, and $h(x)= \min \{f(x), g(x)\}, x \in[-2,2]$. Then $h$ is...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $[t]$ denote the greatest integer $\leq t$. The number of points where the function $f(x)=[x]\left|x^2-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)$ is not continuous is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021 S2
Let $f:[0, \infty) \rightarrow[0,3]$ be a function defined by $...
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
Let $f: R \rightarrow R$ be defined as $...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $f:[0,3] \rightarrow R$ be defined by $f(x)=\min \{x-[x], 1+[x]-x\}$
where $[x]$ is the greatest integer less than or equal to $x$. Let $P$...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f(x)$ be a differentiable function at $x=a$ with $f^{\prime}(a)=2$ and $f(a)=4$. Then $\lim _{x \rightarrow 0} \frac{x f(a)-a f(x)}{x-a}$ equals:
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R$ be defined as $...
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
Let $f: R \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{cc}\frac{x^3}{(1-\cos 2 x)} \log _e\left(\frac{1+2 x e^{-2 x}}{\left(1-x e^{-x}\right)^2}\right), & x \neq 0 \\ \alpha, & x=0\end{array}\right.$....
JEE Main Mathematics Easy
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Q JEE MAIN 2021
A function $f$ is defined on $[-3,3]$ as $$ f(x)=\left\{\begin{array}{cc} \min \left\{|x|, 2-x^2\right\}, & -2 \leq x \leq 2 \\ {[|x|]} & , 2<|x| \leq...
JEE Main Mathematics Medium
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