Question: User: limits
1. **Stating the problem:** We need to understand and evaluate limits in calculus.
2. **Formula and rules:** The limit of a function $f(x)$ as $x$ approaches a value $a$ is written as $$\lim_{x \to a} f(x)$$.
3. **Important rules:**
- If $f(x)$ is continuous at $a$, then $$\lim_{x \to a} f(x) = f(a)$$.
- For rational functions, if direct substitution leads to $\frac{0}{0}$, try factoring or rationalizing.
4. **Example:** Evaluate $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$.
5. **Intermediate work:**
$$\frac{x^2 - 4}{x - 2} = \frac{(x - 2)(x + 2)}{x - 2}$$
6. **Cancel common factors:**
$$\frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = x + 2$$
7. **Evaluate limit:**
$$\lim_{x \to 2} (x + 2) = 2 + 2 = 4$$
8. **Explanation:** We simplified the expression by factoring and canceling the common term, then substituted $x=2$ to find the limit.
**Final answer:** $$4$$