1. **State the problem:** Find the limit of a function as the variable approaches a certain value. Since the user did not specify the exact function or limit, let's consider a general approach to limit problems. 2. **Formula and rules:** The limit of a function $f(x)$ as $x$ approaches $a$ is denoted as $$\lim_{x \to a} f(x) = L$$ if $f(x)$ gets arbitrarily close to $L$ as $x$ approaches $a$. 3. **Important rules:** - If $f(x)$ is continuous at $x=a$, then $$\lim_{x \to a} f(x) = f(a)$$. - For rational functions, if direct substitution leads to an indeterminate form like $\frac{0}{0}$, try factoring, simplifying, or using conjugates. - Use L'Hôpital's Rule if the limit results in $\frac{0}{0}$ or $\frac{\infty}{\infty}$ forms. 4. **Example:** Suppose we want to find $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$. 5. **Intermediate work:** - Factor numerator: $$x^2 - 4 = (x - 2)(x + 2)$$. - Simplify the expression: $$\frac{(x - 2)(x + 2)}{x - 2} = x + 2$$ for $x \neq 2$. 6. **Evaluate the limit:** - Now, $$\lim_{x \to 2} (x + 2) = 2 + 2 = 4$$. 7. **Conclusion:** The limit is 4. This method applies generally: factor and simplify to remove indeterminate forms, then substitute the limit value.