1. The problem is to find the limit of a function as the variable approaches a certain value. 2. The general formula for limits is $$\lim_{x \to a} f(x) = L$$ where $L$ is the value that $f(x)$ approaches as $x$ approaches $a$. 3. Important rules include: - If $f(x)$ is continuous at $x=a$, then $$\lim_{x \to a} f(x) = f(a)$$. - If direct substitution leads to an indeterminate form like $\frac{0}{0}$, use algebraic simplification, factoring, rationalizing, or L'Hôpital's Rule. 4. To solve a specific limit, substitute the value into the function if possible. 5. If substitution is not possible, simplify the expression step-by-step until the limit can be evaluated. 6. Example: Find $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$. - Substitute $x=2$: $$\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ indeterminate. - Factor numerator: $$\frac{(x-2)(x+2)}{x-2}$$. - Cancel $(x-2)$: $$x + 2$$. - Now substitute $x=2$: $$2 + 2 = 4$$. 7. Therefore, $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2} = 4$$. This method applies to many limit problems.