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

[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

 

[Pyrrhus]

It's NOT continuous.

 

[rsnd]

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

 

[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 parallel 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].

 

[HallsofIvy]

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.

 

[matt grime]

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

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.

 

[rsnd]

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