Section 1.4: Continuous Functions
Continuity
Def: A function $f$ is continuous at $c$ when
- $f(c)$ is defined
- $\displaystyle{\lim_{x \to c}}f(x)$ exists and
- $\displaystyle{\lim_{x \to c}}f(x)=f(c)$
$f$ is continuous on $(a,b)$ if it is continuous at each $c$ in $(a,b)$
$f$ is a continuous function if it continuous for each $c$ in its domain.