## Calculus 8th Edition

"Difference Law: The limit of a difference is the difference of the limits" $\lim\limits_{x\to a}[f(x)-g(x)] = \lim\limits_{x \to a}f(x) -\lim\limits_{x \to a}g(x)$ If the individual limits of each function exist. You cannot subtract a limit which does not exist. Thus the statement: $\lim\limits_{x \to 4}[\frac{2x}{x-4}-\frac{8}{x-4}] = \lim\limits_{x \to 4}\frac{2x}{x-4} - \lim\limits_{x \to 4}\frac{8}{x-4}$ Is not true because the individual limits diverge (do not exist)