Let `f(x)={{:((|x-3|)/((x-3))",",xne3),(0",",x=3.):}`
Show that `lim_(xrarr3)f(x)` does not exist.

Explanation

To determine whether the limit \( \lim_{x \to 3} f(x) \) exists, we need to evaluate the left-hand limit (LHL) and the right-hand limit (RHL) of the function \( f(x) \).

### Step 1: Define the function
The function is defined as:
\[
f(x) =
\begin{cases}
\frac{|x-3|}{x-3} & \text{if } x \neq 3 \\
...