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#1 2013-05-20 21:08:40

{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


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

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#2 2013-05-21 07:42:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

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.


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 2013-05-21 14:01:08

{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.


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

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#4 2013-05-21 14:15:16

{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)


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

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#5 2013-05-21 15:06:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

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.

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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#6 2013-05-21 15:32:03

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

Re: Limit related proof

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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#7 2013-05-21 20:57:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

Re: Limit related proof

Hi;

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

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


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.

Offline

#8 2013-05-22 01:31:55

{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.


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

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#9 2013-05-22 05:37:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

Re: Limit related proof

Hi;

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


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.

Offline

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