If `f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):},`show that `lim_(xto0) f(x)` does not exist.

Explanation

To show that the limit of the function \( f(x) \) as \( x \) approaches 0 does not exist, we need to evaluate the left-hand limit and the right-hand limit separately.

### Step 1: Define the function
The function is defined as:
\[
f(x) =
\begin{cases}
\frac{x - |x|}{x} & \text{if } x \neq 0 \\
...