Limits - Examples

Function	Graph	Limits
$f (x) = {\frac{1}{x} \frac{1}{5 ( x - 4 ) ^{2}} x \leq 2 2 < x$		$lim_{x \to 1} f (x) = 1$ $lim_{x \to 0} f (x) = undefined$ $lim_{x \to 4} f (x) = undefined or +\infty$ $lim_{x \to 0^{+}} f (x) = undefined or +\infty$ $lim_{x \to 0^{-}} f (x) = undefined or -\infty$ $lim_{x \to 2} f (x) = undefined$ $lim_{x \to 2^{-}} f (x) = \frac{1}{2}$ $lim_{x \to 2^{+}} f (x) = \frac{1}{20}$
$f (x) = \frac{x - 1}{x - 1}$		$lim_{x \to 1} f (x) = 1$ $f (1) = undefined$

Limits - Properties

$lim_{x \to c} (f (x) + g (x)) = lim_{x \to c} f (x) + lim_{x \to c} g (x)$
$lim_{x \to c} (f (x) - g (x)) = lim_{x \to c} f (x) - lim_{x \to c} g (x)$
$lim_{x \to c} (f (x) \cdot g (x)) = lim_{x \to c} f (x) \cdot lim_{x \to c} g (x)$
$lim_{x \to c} (f (x) / g (x)) = lim_{x \to c} f (x) / lim_{x \to c} g (x)$
$lim_{x \to c} (f (x)^{p}) = (lim_{x \to c} f (x))^{p}$