I need help proving if D is compact, then f/g must be uniformly continuous on D.
Unless there are other hypothsis the statement is false
counter example:
let
$\displaystyle D=[1,3] \mbox{ and } f(x)=x,g(x)=3-x$
Both f and g are uniformly cont on D $\displaystyle \epsilon=1$ will work for all delta but $\displaystyle \frac{f(x)}{g(x)} $
I am thinking that $\displaystyle g(x) \ne 0 $ on D as well.