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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 \( L \neq 0 \), $$ \lim_{x \rightarrow c} \frac{f(x)}{g(x)} = \frac{\lim_{x \rightarrow c} f(x)}{\lim_{x \rightarrow c} g(x)} = \frac{K}{L} $$