Chapter 1.3, Problem 105E

To determine

To calculate: Two functions $f\left(x\right)$ and $g\left(x\right)$ such that $\underset{x\to 0}{\lim }f\left(x\right)\text{and}\underset{x\to 0}{\lim }g\left(x\right)$ so that both do not exist but $\underset{x\to 0}{\lim }\left(f\left(x\right)+g\left(x\right)\right)$ exist.