Chapter 2.7, Problem 63E

Suppose $\underset{x\to a}{\lim }f\left(x\right)=\infty$ and $\underset{x\to a}{\lim }\left(x\right)=\infty$. Prove that $\underset{x\to a}{\lim }\left(f\left(x\right)+g\left(x\right)\right)=\infty$.