1. The problem asks: What does $\lim_{x \to a} f(x) = L$ mean? 2. The limit definition states: As $x$ approaches $a$, the function values $f(x)$ approach $L$. 3. Important rule: The limit describes the behavior of $f(x)$ near $a$, not necessarily the value at $a$. 4. Explanation of options: - a) Correct: As $x$ gets closer to $a$, $f(x)$ gets closer to $L$. - b) Incorrect: The limit does not require $f(a) = L$. - c) Incorrect: Continuity requires the limit equals the function value, but the limit alone does not guarantee continuity. - d) Incorrect: The function may or may not be defined at $a$. Final answer: a) As $x$ gets closer to $a$, the value of $f(x)$ gets closer to $L$.