If f(c) = infinity and c is in [a,b]

1. May 8, 2005

rsnd

if f(c) = infinity and c is in [a,b]
is it equivalent to saying
f is not cont. at c ??? because infinity is undefined???

Thanks
k.cv

2. May 8, 2005

Pyrrhus

It's NOT continuous.

3. May 8, 2005

rsnd

SO it would also imply that if a function is cont. in a finite interval [a,b] then its bounded?

4. May 8, 2005

Pyrrhus

Yes, it has superior bound. There exist a number N such that f(x)<= N for every x in [a,b]. Geometricly speaking this means there exist a paralel line to the horizontal axis. And of course a inferior bound, the same for a number N such that f(x) >= N for every x in [a,b].

Last edited: May 8, 2005
5. May 8, 2005

HallsofIvy

Staff Emeritus
If a function f is continuous on a closed and bounded interval, then it is bounded. You implied "closed" when you said [a,b] but I want to make sure that is clear.

Last edited: May 8, 2005
6. May 8, 2005

matt grime

If you're claiming f is a function from [a,b] to R, then f is not defined at c, and actually f therefore isn't a function, never mind a continuous one.

7. May 13, 2005

rsnd

nice...I just invented the mean value theorom!!