# AoMath: Limit Laws

IF
$$\lim_{x \rightarrow c} f(x) = K$$ $$\lim_{x \rightarrow c} g(x) = L$$
$$M,N$$ are real numbers and are constants

THEN
$$\lim_{x \rightarrow c} M = M$$ $$\lim_{x \rightarrow c} M\cdot N = \lim_{x \rightarrow c} M \cdot \lim_{x \rightarrow c} N = MN$$ $$\lim_{x \rightarrow c} M\cdot f(x) = \lim_{x \rightarrow c} M \cdot \lim_{x \rightarrow c} f(x) = M \cdot \lim_{x \rightarrow c} f(x) = MK$$ $$\lim_{x \rightarrow c} f(x) + g(x) = \lim_{x \rightarrow c} f(x) + \lim_{x \rightarrow c} g(x)= K + L$$ $$\lim_{x \rightarrow c} f(x) - g(x) = \lim_{x \rightarrow c} f(x) - \lim_{x \rightarrow c} g(x) = K - L$$ $$\lim_{x \rightarrow c} f(x)\cdot g(x) = \lim_{x \rightarrow c} f(x) \cdot \lim_{x \rightarrow c} g(x) = KL$$ If ALSO $$\lim_{x \rightarrow c} g(x) \neq 0$$ and/or $$L \neq 0$$, $$\lim_{x \rightarrow c} \frac{f(x)}{g(x)} = \frac{\lim_{x \rightarrow c} f(x)}{\lim_{x \rightarrow c} g(x)} = \frac{K}{L}$$