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#26 2012-01-21 07:48:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym

i would say e^n,but don't know why.


“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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#27 2012-01-21 07:52:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Correct! You could take the limit of the ratio of them.


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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#28 2012-01-21 07:53:30

anonimnystefy
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Posts: 14,886

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

ok.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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#29 2012-01-21 07:55:21

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

What is being said in the above statement? if x = .1 how accurate do you expect that series to be?


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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#30 2012-01-21 08:01:33

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

if i'm not wrong that's the approximation of the sin(x) function.

well it means that |sin(x)-x+x^3/6-x^5/120|<c*x^6 for some const. c>0

i expect the value of x-x^3/6+x^5/120 to be at most 1 away from the value we wanted to calculate in the first place.


“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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#31 2012-01-21 08:04:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

The first part is correct. I do not like the second part.


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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#32 2012-01-21 08:04:51

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

me neither.


“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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#33 2012-01-21 08:07:03

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Compute Sin[.1]


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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#34 2012-01-21 08:12:08

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym

i didn't see the decimal point.well my second guess would be 10^(-6) but i'm not sure that one's correct either.could you tell me how it's 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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#35 2012-01-21 08:12:59

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Yes, but it is better if you see it for yourself. Start by computing Sin[.1].


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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#36 2012-01-21 08:14:25

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

i have nothing against doing it by myself.just walk me through it.

sin(0.1)=0.0998... approx. 0.1

Last edited by anonimnystefy (2012-01-21 08:23:08)


“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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#37 2012-01-21 08:14:26

John E. Franklin
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Registered: 2005-08-29
Posts: 3,562

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

Use radians?


igloo myrtilles fourmis

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#38 2012-01-21 08:21:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Hi;

That is not correct, please be a little more careful and I am walking you through it.

Hi John;

Yes, it is in radians.


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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#39 2012-01-21 08:23:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym

i forgot a zero by accident.fixed it 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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#40 2012-01-21 08:26:50

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

You will need more decimal places for this example.


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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#41 2012-01-21 08:29:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

ok then.can do. 0.0998334.i think it's enough.

Last edited by anonimnystefy (2012-01-21 08:29:37)


“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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#42 2012-01-21 08:30:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Now compute using that series the value .1


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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#43 2012-01-21 08:36:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

0.0998334...the same

i used alpha.it says the difference is about 2*10^(-11)

Last edited by anonimnystefy (2012-01-21 08:36:38)


“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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#44 2012-01-21 21:22:19

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Hi anonimnystefy;

Power went out for many hours and is only intermittent right now, sorry for the delay.

Here is a new question.
Big O gave us an error estimate of about 10^-6 we can see that the error is much smaller than that, about 10^-11. Can you explain that?


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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#45 2012-01-22 01:50:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym

well Big Oh gives us the maximum difference between the real value and the estimated value.

that's why it's |sin(x)-f(x)|<x^6 where f(x) is a function of x i wrote above.
                                      ^
                                       |
                                       |this here says so.the abs. difference of the real function value and the approx. value is less that x^6 for every x we have.


“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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#46 2012-01-22 02:04:57

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Also Big O does not care about a constant multiple that could be large. It is only concerned about the asymptotic properties.


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.

Offline

#47 2012-01-22 02:09:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym

next one please.

btw,i just found out that the number coming out of justlookingforthemoment's saxophone av is a Harshad number.


“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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#48 2012-01-22 02:19:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Show that f(n)= (n+2)^3 is O(n^3)


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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#49 2012-01-22 02:22:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,886

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

hi bobbym


so (n+2)^3 is O(n^3)

Last edited by anonimnystefy (2012-01-22 02:23:12)


“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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#50 2012-01-22 02:30:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

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

Hi;

Or:

Now because (n+2)^3 ≤ 8n^3 when n>1

An application:
I wish to evaluate e^(-.1) using a taylor series to an error less than .000001 how can I do that?


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.

Offline

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