Example:

• From the left ($x < 3$), $|x - 3| = -(x - 3)$ $\to$ value = $-1$
• From the right ($x > 3$), $|x - 3| = x - 3$ $\to$ value = $1$

Since the two one-sided limits aren't equal, the limit does not exist.

This is a classic example of a jump discontinuity, where the function abruptly switches values at a point.