Let $f:R\rightarrow R$ be a function defined by $f\left(x\right)=Min \left\{x+1, \left|x\right|+1\right\}$. Then which of the following is true?

Consider the following in respect of the function $f(x) = \left\{\begin{matrix}2+ x, & x \geq 0\\ 2 - x, & x < 0\end{matrix}\right.$

1. $\displaystyle \lim_{x \rightarrow 1} f(x)$ does not exist.

2. f(x) is differentiable at x = 0.

3. f(x) is continuous at x = 0.

Which of the above statements is/are correct?

The function $f(x)=|x|+|x-1|$ is

Which of the following function is thrice differentiable at x=0?