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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi anonimnystefy;

That thread got closed by mistake. It is open now for business.

Did you get as far as a catenary? If you find the equation of the catenary and Taylorize it you will be close. See if you can get it from there. Tell me what you think about it.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

i found that it's y=cosh(x)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

But you must get the series for it and then you will see.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

it's x+x^3/3!+x^5/5!+...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That is not correct.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

sry.copied the wrong series.

1+x^2/2!+x^4/4!+...

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi

what about?i see the pic.it looks parabolish.

Now what can you say about that? Be right back!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

don't now.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Look at the first two terms of the Mclaurin series, what do you see?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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x^2/2 +1,which is a parabola.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

That is correct! Since that series is an approximation of cosh(x) anywhere we truncate it, is also an approximation. The further we go the better we expect to do. Now you see why Galilieo was fooled into thinking the catenary was a parabola.

That series is a good approximation at x = 0 and close to that. How about for any x?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

hi bobbym

it's not so good for very large terms because the difference grows 'cubicly' so as x gets larger,the difference becomes much much larger.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Yes, that is true for that particular series.You can get around that and we are just trying to demonstrate that a parabola is a good approximation. We do not need a high precision algorithm.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

yup.

next?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hold it! You did not provide any indication that it is so.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

hi bobbym

|cosh(x)-1-x^2/2|<c*|x^3|

so (cosh(x)-1-x^2/2) is O(x^3).thus,my statement is correct.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, but that is only the expansion around zero. It is not the series that we want at 5 for an example.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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maybe we could take the taylor's series expansion arounf 5 or a in a general case.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Exact a Mundo! We can expand around c.

Now since cosh(c) and sinh(c) are constants we can substitute. a = cosh(c) and b = sinh(c).

Truncating at x^2 we get:

which again means for any value of x it can be approximated by a quadratic. This is not exactly true in a rigorous sense but for the purposes of your question we will allow it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

nice!

next?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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What next? You are done for now!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

next question?i'm not done.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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It will take me some time to think of one. I think the other question you have in the other will be a good source of more questions.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

ok,but i will need help with it.that's of course assuming that you mean the one with the squares and stuff.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

I disagree, you can do it all by yourself. I do not know the answer right now either.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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