Definition of Continuity

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 $ε - δ$ , for any $ε > 0$ , there exists a $δ > 0$ such that we have

| f (x) - f (a) | < ε

whenever $

x-a

<\delta$.