limit laws

The algebraic rules — sum, product, quotient, power — that let limits of combined functions be computed from limits of their pieces.

The limit laws say that if $\lim_{x\to a} f(x)$ and $\lim_{x\to a} g(x)$ both exist, then the limit of $f+g$ , $f-g$ , $fg$ , $f/g$ (denominator limit nonzero), and $f^n$ can each be computed by combining the individual limits the same way — limit of a sum is the sum of the limits, and so on.

Examples

$\displaystyle\lim_{x\to 3}(x^2+2x) = \lim_{x\to3}x^2 + \lim_{x\to3}2x = 9+6=15$ .