We say a function $f(x)$ is continuous at $x=a$ if $f$ satisfies
\[\lim_{x\to a^+}f(x)=\lim_{x\to a^-}=f(a).\]In terms of $\varepsilon-\delta$, for any $\varepsilon>0$, there exists a $\delta>0$ such that we have
\[|f(x)-f(a)|<\varepsilon\]| whenever $ | x-a | <\delta$. |