Finding the Limit of a Difference

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 \[ \begin{equation*} \lim_{x\rightarrow 4}(6-x)=\lim_{x\rightarrow 4}6-\lim_{x\rightarrow 4}x=6-4=2 \end{equation*} \]