Continuity

Sidedness

Left continuity at $c$ if $lim_{x \to c^{-}} f (x) = f (c)$
Right continuity at $c$ if $lim_{x \to c^{+}} f (x) = f (c)$

$f @ g$ is continuous at $c$ , where $@$ is any of addition, subtraction, multiplication or division (when $@$ = division, $g (c) \neq 0$ ), if $f$ and $g$ are continuous at $c$
$f \circ g$ is continuous at $c$ if $g$ is continuous at $c$ and $f$ is continuous at $g (c)$
Functions continuous over their domain:
- Polynomials
- Rational functions
- Root functions
- Trigonometric functions
- Inverse trigonometric functions
- Exponential functions
- Logarithmic functions

To find if $f (x)$ is continuous at $c$ , evaluate $lim_{x \to c} f (x) = f (c)$ .

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