1. The problem is to find the limit of a function as the variable approaches a certain value. 2. A common formula used is $$\lim_{x \to a} f(x) = L$$ where $L$ is the value the function approaches as $x$ approaches $a$. 3. Important rules include: - If direct substitution gives a finite number, that is the limit. - If substitution gives an indeterminate form like $\frac{0}{0}$, use algebraic simplification or L'Hôpital's Rule. 4. Example question: Find $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$. 5. Substitute $x=2$: $$\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ which is indeterminate. 6. Factor numerator: $$\frac{(x-2)(x+2)}{x-2}$$. 7. Cancel common factor $(x-2)$: $$x + 2$$. 8. Now substitute $x=2$: $$2 + 2 = 4$$. 9. Therefore, $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2} = 4$$. This is a typical limit problem involving factoring and simplification.