Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 1: Assam CEE 2016

Let $f\left(x\right)=\frac{\sin \left(\pi \left[x+\pi \right]\right)}{1+{\left[x\right]}^2}$, (where $\left[·\right]$ denotes the greatest integer function). Then $f\left(x\right)$ is a:

Consider the function $f\left(x\right)=x-\left|x-x^2\right|,-1\le x\le 2$. The points of discontinuities of $f\left(x\right)$  are 

The set of points, where the function $f\left(x\right)=\frac{x}{1+\left|x\right|}$ is differentiable, is

Which of the following functions is differentiable at $x=0?$