If $f$ and $g$ are functions for which $\lim _{x \rightarrow c} f(x)$ and $\lim _{x \rightarrow c} g(x)$ both exist, then $\lim _{x \rightarrow c}[f(x) \pm g(x)]$ exists and $\lim _{x \rightarrow c}[f(x) \pm g(x)]=\lim _{x \rightarrow c} f(x) \pm \lim _{x \rightarrow c} g(x)$