If `f(x)=[|x|+1, x<0 0, x=0|x|-1, x >0`

Explanation

To determine whether the limit \( \lim_{x \to a} f(x) \) exists for the piecewise function defined as:

\[
f(x) =
\begin{cases}
|x| + 1 & \text{if } x < 0 \\
0 & \text{if } x = 0 \\
|x| - 1 & \text{if } x > 0
...