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

My friend wants proof of this statement but i don't know how to prove it,can anyone help- If the limit of g(x) as x tends to a is b than the limit of f(g(x)) as x tends to a and the limit of f(y) as y tends to b is same

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,311

Hi {7/3};

I probably am misunderstanding you but I am getting:

I am assuming f(x) is an arbitrary function since you did not specify one.

Let's say a = 1.

so b=2,

Which is a counterexample.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

No,i meant limit of f(g(x)) as x approaches a is equal to limit of f(y) as y approaches b.

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

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

If

then*Last edited by {7/3} (2013-05-21 14:18:15)*

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,311

Hi;

Use the composition law for limits:

If x is continuous at b and

then

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

I think he wants proof of the composition law

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,311

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Thanks,bobbym,my friend liked the proof and i liked the link.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,311

Hi;

It is a nice link, alot of good explanation there.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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