#1
Alright I know there's a math thread but I can't really wait around for hours.
Anyone that is good with limits will be able to help me out.

Show that f is continuous on (-infinity,infinity)

f(x)=x^2 if x<1
f(x)=rootx if x > or equal to 1

I REALLY don't get this question, if someone could explain how to do this maybe? I have solution but I don't get it.


EDIT: Shi t never mind...I get it now after reading the solution like ten times.,,
Sorry.
#2
So did you just graph it or what? How else would you show it? Limits? I'm just curious.
My Rig:
Epiphone Les Paul Custom - Alpine White
Vox AD30VT
Epiphone SG Special - Black
Planet Waves Cables
Levy's Strap
Dunlop .70 Picks
#4
do the limit as x aproaches -infinity, and as x aproaches infinity ?
sigh...
#5
Dang dude I've never done that. What level Calculus is that?
My Rig:
Epiphone Les Paul Custom - Alpine White
Vox AD30VT
Epiphone SG Special - Black
Planet Waves Cables
Levy's Strap
Dunlop .70 Picks
#6
It's pretty easy, you just have to be able to make sense of it all. Explaining it will be good for my knowledge.
Ok, so, all you have to do is say,
x^2 is continuous from negative infinity to 1, and root x is continuous from 1 to positive infinity. from that you know the function is continuous throughout.
you prove this by saying the limit of x^2 as x approaches on from the left side equals one, and the limit of rootx as x approaches one from the right side equals one, therefore the limit of f(x) as x approaches one is continous.
Once you have that, it is just a matter of combining the domains, because x^2 is continuous from negative infinity to 1, and rootx is continuous from 1 to positive infinity, and they are equal, therefore their domains are equal, so therefore f is continuous from negative infinity to positive infinity.
make sense?
Last edited by tona_107 at Oct 1, 2008,
#7
and it's university level.
You could graph it but I don't think that would get you full marks.
If you did the limits as it equals infinity, I'm not sure what you'd get, but it wouldn't be the answer.
#9
We all good? Awesome, I'm reporting this. Also, For future reference, Maths and Physics thread
in the stickies.


*Reported*
#10
Quote by tona_107
It's pretty easy, you just have to be able to make sense of it all. Explaining it will be good for my knowledge.
Ok, so, all you have to do is say,
x^2 is continuous from negative infinity to 1, and root x is continuous from 1 to positive infinity. from that you know the function is continuous throughout. you prove this by saying the limit of x^2 as x approaches on from the left side equals one, and the limit of rootx as x approaches one from the right side equals one, therefore the limit of f(x) as x approaches one is continous. Once you have that, it is just a matter of combining the domains, because x^2 is continuous from negative infinity to 1, and rootx is continuous from 1 to positive infinity, and they are equal, therefore their domains are equal, so therefore f is continuous from negative infinity to positive infinity.
make sense?


You answered your own question.

/thread
Quote by Tyler Durden
It's only after we've lost everything that we're free to do anything.

Erowid