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 $$\begin{equation*} \lim_{x\rightarrow -3}(x+4)=\lim_{x\rightarrow -3}x+\lim_{x\rightarrow -3}4=-3+4=1 \end{equation*}$$