| Definition: Suppose $f(x)$ is defined for all $x$ near $a$ (possibly excluding $a$). $$ \lim_{x \rightarrow a} f(x) = L$$ (read: "the limit of $f(x)$, as $x$ approaches $a$, equals $L$") means that we can get $f(x)$ as close to $L$ as we want by making $x$ sufficiently close to $a$. |
The following video explores what this means graphically.