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#151 2012-01-27 02:41:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Oh,Oh,Oh,merry analysis!!!

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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#152 2012-02-11 02:56:40

anonimnystefy
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Re: Oh,Oh,Oh,merry analysis!!!

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#153 2012-02-11 06:30:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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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#154 2012-02-11 06:42:14

anonimnystefy
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Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#155 2012-02-11 06:47:59

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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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#156 2012-02-11 07:09:29

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

sry.copied the wrong series.

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#157 2012-02-11 07:11:02

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

Hi

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

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


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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#158 2012-02-11 07:20:35

anonimnystefy
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Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

don't now.


“Here lies the reader who will never open this book. He is forever dead.

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

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#159 2012-02-11 07:21:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

Look at the first two terms of the Mclaurin series, what do you 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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#160 2012-02-11 07:24:20

anonimnystefy
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Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

x^2/2 +1,which is a parabola.


“Here lies the reader who will never open this book. He is forever dead.

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

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#161 2012-02-11 07:27:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Oh,Oh,Oh,merry analysis!!!

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?


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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#162 2012-02-11 07:47:00

anonimnystefy
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Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

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.


“Here lies the reader who will never open this book. He is forever dead.

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

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#163 2012-02-11 07:51:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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.


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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#164 2012-02-11 07:52:28

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

yup.

next?


“Here lies the reader who will never open this book. He is forever dead.

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

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#165 2012-02-11 07:53:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

Hold it! You did not provide any indication that it is so.


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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#166 2012-02-11 07:58:17

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

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.


“Here lies the reader who will never open this book. He is forever dead.

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

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#167 2012-02-11 07:59:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

Yes, but that is only the expansion around zero. It is not the series that we want at 5 for an example.


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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#168 2012-02-11 08:04:06

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

maybe we could take the taylor's series expansion arounf 5 or a in a general case.


“Here lies the reader who will never open this book. He is forever dead.

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

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#169 2012-02-11 08:10:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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.


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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#170 2012-02-11 08:13:15

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

nice!

next?


“Here lies the reader who will never open this book. He is forever dead.

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

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#171 2012-02-11 08:14:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

What next? You are done for now!


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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#172 2012-02-11 08:15:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

next question?i'm not done.


“Here lies the reader who will never open this book. He is forever dead.

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

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#173 2012-02-11 08:17:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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.


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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#174 2012-02-11 08:19:59

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Oh,Oh,Oh,merry analysis!!!

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#175 2012-02-11 08:22:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,215

Re: Oh,Oh,Oh,merry analysis!!!

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


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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