Chapter 1.6, Problem 63E

Show by means of an example that ${{\displaystyle \lim }}_{x\to a}\left[f\left(x\right)g\left(x\right)\right]$ may exist even though neither ${{\displaystyle \lim }}_{x\to a}f\left(x\right)$ nor ${{\displaystyle \lim }}_{x\to a}g\left(x\right)$ exists.