Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 2: Level 2

Let $g$ be the greatest integer function. Then the function $f\left(x\right)={\left(g\left(x\right)\right)}^2-g\left(x\right)$ is discontinuous at

The number of points, at which the function $f\left(x\right)=\left|2x+1\right|-3\left|x+2\right|+\left|x^2+x-2\right|,x\in R$ is not differentiable, is

For each $x\in R,$ let $f\left(x\right)=|x-1|, g\left(x\right)=\cos x$ and $\varphi \left(x\right)=f\left(g\right(2\sin x\left)\right)-g\left(f\right(x).$ Then $\varphi$ is

For $f\left(x\right)=\left\{\begin{array}{cc}x\frac{e^{\frac{1}{x}}-e^{\frac{-1}{x}}}{e^{\frac{1}{x}}+e^{\frac{-1}{x}}},& x\ne 0\\ 0,& x=0\end{array}\right.$

Rolle's theorem is not applicable for which of the following functions?

For the function $x+\frac{1}{x},x\in [1,3],$ the value of $c$ for the mean value theorem is

The equation, $\sin x+2\sin 2x+3\sin 3x=\frac{8}{\pi }$ has at least one root in

Let $f^{\text{'}}\left(x\right)=e^{x^2}$ and $f\left(0\right)=10 .$ If $A<f\left(1\right)<B$ can be concluded from the mean value theorem, then the largest value of $(A-B)$ equals