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#1 2013-05-19 18:43:24

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Continuous functions

I have been give a function f(x)=3x^3+x-2,how do i show it is a continuous function?


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#2 2013-05-19 22:03:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,654

Re: Continuous functions

Hi;

All polynomials are continuous.

You might try here and see if you like his proof:

http://www.proofwiki.org/wiki/Polynomial_is_Continuous


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2013-05-19 22:28:07

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: Continuous functions

I'd love to go to that link but for some reason the link's words look weired and i can't read them.


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#4 2013-05-19 22:42:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,654

Re: Continuous functions

Hi;

Okay, I have a snapshot of it:

Let's see if these will suffice because they are simpler than epsilon delta type proofs.

I am assuming you are talking about continuity in R.

View Image: 2013-05-20_033954.gif View Image: 2013-05-20_034102.gif

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2013-05-19 23:43:08

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: Continuous functions

Thanks a lot bobbym


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#6 2013-05-19 23:47:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,654

Re: Continuous functions

Hi;

It is really going to depend on how far back they want you to go. If they will accept that any linear function ( ax + b ) is continuous then we are done with the above. If not, you may have to prove the theorem on linear functions first.

Also, somebody else might have a better idea.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2013-05-20 00:23:29

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: Continuous functions

I know how to prove linear functions are continuous


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#8 2013-05-20 00:27:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,654

Re: Continuous functions

Hi;

Then I think we are done here...


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2013-05-20 01:14:59

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

Re: Continuous functions

hi {7/3}

in post 3 you  wrote:

I'd love to go to that link but for some reason the link's words look weired and i can't read them.

The maths appears to be in a Latex like code.  Maybe your browser isn't set to view it properly.  Try View Source.

And I found it took a while for all the code to be interpreted correctly.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2013-05-20 01:28:02

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: Continuous functions

Thanks for the advice,bob bundy,i will try it.


There are 10 kinds of people in the world,people who understand binary and people who don't.

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