Discontinuity

① jump discontinuity

$f(x)= {2x \space where \space x \le 1 \brace -x+2 \space where \space x>1 }$

② removable discontinuity

$f(x)= \frac {(x-3)^2(x-4)} {x-4}$

③ infinite discontinuity

$f(x) = \frac {1}{x-2}$

④ wild discontinuity

$f(x) = cos(\frac {1} {x})$

Continuity at a Point

a function $f$ is continuous at ${x=a}$ if

① $\lim\limits_{x \to a} fx$ exists

② $f(a)$ exists

③ $\lim\limits_{x \to a} fx = f(a)$

有時就是用第三個表示而已，當作 1, 2 都符合。