1. The problem asks: What does $\lim_{x \to a} f(x) = L$ mean? 2. The limit notation $\lim_{x \to a} f(x) = L$ means that as $x$ gets closer and closer to the number $a$, the values of the function $f(x)$ get closer and closer to the number $L$. 3. Important rule: The limit describes the behavior of $f(x)$ near $a$, but not necessarily at $a$ itself. 4. For example, if $f(x)$ approaches 5 as $x$ approaches 2, we write $\lim_{x \to 2} f(x) = 5$. 5. This means if you pick $x$ values very close to 2 (but not equal to 2), $f(x)$ values will be very close to 5. 6. So, the limit tells us the value the function is approaching, even if the function is not defined at $a$ or has a different value there. Final answer: $\lim_{x \to a} f(x) = L$ means the function values get closer to $L$ as $x$ gets closer to $a$.