Chapter 14.2, Problem 50E

To determine

Toprove:

if $f\left(x\right)$ is continuous at $x=a$ and $g\left(y\right)$ is continuous at $y=b$, then $F\left(x,y\right)=f\left(x\right)g\left(y\right)$ is continuous at $\left(a,b\right)$.