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Continuity and Differentiability

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2020
Let $f(x)=x \cdot\left[\frac{x}{2}\right]$ for $-10
JEE Main Mathematics Easy
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Q JEE MAIN 2020
The position of a moving car at time $t$ is given by $f(t)=a t^2+b t+c, t>0$, where $a, b$ and $c$ are real numbers greater...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
JEE Main Mathematics Easy
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Q JEE MAIN 2020
If the function $f(x)\left\{\begin{array}{ll}k_1(x-\pi)^2-1, & x \leq \pi \\ k_2 \cos x, & x>\pi\end{array}\right.$ is twice differentiable, then the ordered pair $\left(k_1, k_2\right)$ is equal...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $f: R \rightarrow R$ be a function defined by $f(x)=\max \left\{x, x^2\right\}$. Let $S$ denote the set of all points in $R$, where $f$...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
If $f(x+y)=f(x) f(y)$ and $\sum_{x=1}^{\infty} f(x)=2 x, y \in N$, where $N$ is the set of all natural numbers, then the value of $\frac{f(4)}{f(2)}$ is...
JEE Main Mathematics Easy
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Q JEE MAIN 2019
Let $f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x<0 \\ x^2-1, & 0 \leq x \leq 2\end{array}\right.$ and
g(x) = | f(x)|+f(|x|). Then, in the interval (–2, 2),...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $[t]$ denote the greatest integer $\leq t$ and $\lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A$. Then the function, $f(x)=\left[x^2\right] \sin (\pi x)$ is discontinuous, when x...
JEE Main Mathematics Easy
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Q JEE Main 2019
Let $f(x)=\left\{\begin{array}{ll}\max \left\{|x|, x^2\right\}, & |x| \leq 2 \\ 8-2|x|, & 2<|x| \leq 4\end{array}\right\}$ Let $S$ be the set of points in the interval $(-4,4)$...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y)=f(x)+f(y)+x y^2+x^2 y$, for all real $x$ and $y . \lim _{x \rightarrow 0} \frac{f(x)}{x}=1$, If then...
JEE Main Mathematics Medium
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