Math Is Fun Forum

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Limit related proof

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

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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: Limit related proof

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.

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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: Limit related proof

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

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

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Limit related proof

If

then

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

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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: Limit related proof

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.
Always satisfy the Prime Directive of getting the right answer above all else.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Limit related proof

I think he wants proof of the composition law

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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: Limit related proof

Hi;

This is what I use, maybe he will like it.

http://www.milefoot.com/math/calculus/l … oofs04.htm

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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: Limit related proof

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

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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: Limit related proof

Hi;

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

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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.