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#1 2013-05-21 19:08:40

{7/3}
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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.

#2 2013-05-22 05:42:52

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-05-22 12:01:08

{7/3}
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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.

#4 2013-05-22 12:15:16

{7/3}
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Re: Limit related proof

If

then

Last edited by {7/3} (2013-05-22 12:18:15)


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

#5 2013-05-22 13:06:01

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-05-22 13:32:03

{7/3}
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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.

#7 2013-05-22 18:57:34

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2013-05-22 23:31:55

{7/3}
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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.

#9 2013-05-23 03:37:05

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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