Show that, `lim_(xto4) (|x-4|)/(x-4)`, does not exist

Explanation

To show that the limit \( \lim_{x \to 4} \frac{|x-4|}{x-4} \) does not exist, we need to evaluate both the left-hand limit and the right-hand limit as \( x \) approaches 4.

### Step 1: Evaluate the Left-Hand Limit
We start by finding the left-hand limit, which is denoted as:
\[ \lim_{x \to 4^-} \frac{|x-4|}{x-4} \]
When \( x \) approaches 4 from the left (i.e., \( x < 4 \)), the expression \( x - 4 \) is negative. Therefore, we can rewrite the absolute value:
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