Find $\lim\limits_{x\rightarrow 4} (6-x)$.

Solution $F(x)=6-x$ is the difference of two functions $f(x)=6$ and $g(x)=x$. $$\lim_{x\rightarrow 4}f(x)=\lim_{x\rightarrow 4}6=6\qquad \hbox{and}\qquad \lim_{x\rightarrow 4}g(x)=\lim_{x\rightarrow 4}x=4$$

Then, using the Limit of a Difference, we have $$\begin{equation*} \lim_{x\rightarrow 4}(6-x)=\lim_{x\rightarrow 4}6-\lim_{x\rightarrow 4}x=6-4=2 \end{equation*}$$