Show that `lim_(xrarr2) ([x-2])/(x-2)` does not exist.

Explanation

To show that the limit \( \lim_{x \to 2} \frac{|x-2|}{x-2} \) does not exist, we will evaluate the left-hand limit and the right-hand limit at \( x = 2 \).

### Step 1: Define the function based on the absolute value
The expression \( |x-2| \) can be defined piecewise:
- If \( x < 2 \), then \( |x-2| = -(x-2) = 2-x \).
- If \( x \geq 2 \), then \( |x-2| = x-2 \).

### Step 2: Calculate the left-hand limit as \( x \) approaches 2
...