If $f$ and $g$ are functions for which $\lim _{x \rightarrow c} f(x)$ and $\lim _{x \rightarrow c} g(x)$ both exist then $\lim _{x \rightarrow c}[f(x) \cdot g(x)]$ exists and $\lim _{x \rightarrow c}[f(x) \cdot g(x)]=\lim _{x \rightarrow c} f(x) \cdot \lim _{x \rightarrow c} g(x)$ #### Corollary: Limit of a Constant Times a Function If $g$ is a function for which $\lim _{x \rightarrow c} g(x)$ exists and if $k$ is any real number, then $\lim _{x \rightarrow c}[k g(x)]$ exists and $ \lim _{x \rightarrow c}[k g(x)]=k \lim _{x \rightarrow c} g(x) $ #### Corollary: Limit of a Power If $\lim _{x \rightarrow c} f(x)$ exists and if $n \geq 2$ is an integer, then $ \lim _{x \rightarrow c}[f(x)]^{n}=\left[\lim _{x \rightarrow c} f(x)\right]^{n} $