1. The problem is to understand the limit notation $\lim_{x \to a}$ and what it represents. 2. The limit $\lim_{x \to a} f(x)$ describes the value that the function $f(x)$ approaches as $x$ gets arbitrarily close to $a$. 3. Important rules include: - The limit may exist even if $f(a)$ is not defined. - The limit can be finite or infinite. - To find the limit, we analyze the behavior of $f(x)$ near $a$, not necessarily at $a$. 4. For example, if $f(x) = x^2$, then $\lim_{x \to 3} x^2 = 9$ because as $x$ approaches 3, $x^2$ approaches 9. 5. To evaluate a limit, substitute $x = a$ if the function is continuous at $a$; otherwise, use algebraic simplification, factoring, or special limit laws. 6. This notation is fundamental in calculus for defining derivatives and continuity.