Math Is Fun Forum

{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?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

{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.

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Continuous functions

Thanks a lot bobbym

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Continuous functions

I know how to prove linear functions are continuous

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Continuous functions

Hi;

Then I think we are done here...

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Continuous functions

hi {7/3}

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Continuous functions

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

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