1. **Problem 1:** Find the limit $$\lim_{x \to 3^-} \frac{|x-3|}{x-3}$$. The expression involves the absolute value function and a denominator that approaches zero from the left side. 2. **Formula and rules:** - For $x < 3$, $|x-3| = 3 - x$ because the expression inside the absolute value is negative. - The limit from the left means $x$ approaches 3 with values less than 3. 3. **Evaluate the limit:** For $x \to 3^-$, $$\frac{|x-3|}{x-3} = \frac{3 - x}{x - 3}$$ 4. Simplify the fraction: $$\frac{3 - x}{x - 3} = \frac{-(x - 3)}{x - 3} = -\frac{x - 3}{x - 3}$$ 5. Cancel common factors: $$-\frac{\cancel{x - 3}}{\cancel{x - 3}} = -1$$ 6. **Answer:** $$\lim_{x \to 3^-} \frac{|x-3|}{x-3} = -1$$