Chapter 1.3, Problem 105E

Finding Functions Find two functions f and g such that $\underset{x\to 0}{\lim }f\left(x\right)$ and $\underset{x\to 0}{\lim }g\left(x\right)$ do not exist, but

$\underset{x\to 0}{\lim }\left[f\left(x\right)+g\left(x\right)\right]$ does exist.