I'm looking for some help with proving that if f and g are continuous then so is f/g. I need to use the ε and Δ definition of continuity
( │ x - a│< Δ implies │f(x) – f(a)│< ε) to prove this.
I'm looking for some help with proving that if f and g are continuous then so is f/g. I need to use the ε and Δ definition of continuity
( │ x - a│< Δ implies │f(x) – f(a)│< ε) to prove this.
Of course, we must assume , and then :
We also have that , thus for :
, where K is a
constant (as g(x) is as close to g(a) as we want if x close enough to a).