$\lim _{x \rightarrow c^{-}} f(x)=L_{\mathrm{left}}$ $\lim _{x \rightarrow c^{+}} f(x)=L_{\text {right}}$ The limit $L$ of a function $y=f(x)$ as $x$ approaches a number $c$ exists if and only if both one-sided limits exist at $c$ and both one-sided limits are equal. That is, $ \lim _{x \rightarrow c} f(x)=L \text { if and only if } \lim _{x \rightarrow c^{-}} f(x)=\lim _{x \rightarrow c^{+}} f(x)=L $