1. Problem: Find the value of the limit $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$. 2. Formula: The limit of a function as $x$ approaches a value $a$ is the value that $f(x)$ approaches as $x$ gets closer to $a$. 3. Important rule: If direct substitution results in an indeterminate form like $\frac{0}{0}$, try to simplify the expression. 4. Work: $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2} = \lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}$$ 5. Cancel common factor: $$\lim_{x \to 2} \frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = \lim_{x \to 2} (x + 2)$$ 6. Substitute $x = 2$: $$2 + 2 = 4$$ 7. Final answer: The limit is $4$. This problem demonstrates how to evaluate limits by factoring and canceling common terms to resolve indeterminate forms.