Finding the Limit of a Sum

Find \(\lim\limits_{x\rightarrow -3}(x+4)\).

Solution \(F(x)=x+4\) is the sum of two functions \(f(x)=x\) and \( g(x)=4\). From the limits given in (1) and (2), we have \[ \begin{equation*} \lim_{x\rightarrow -3}f(x)=\lim_{x\rightarrow -3}x=-3\qquad \hbox{and}\qquad \lim_{x\rightarrow -3}g(x)=\lim_{x\rightarrow -3}4=4 \end{equation*} \]

Then, using the Limit of a Sum, we have \[ \begin{equation*} \lim_{x\rightarrow -3}(x+4)=\lim_{x\rightarrow -3}x+\lim_{x\rightarrow -3}4=-3+4=1 \end{equation*} \]