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

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

hi bobbym

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


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#27 2012-01-21 07:52:34

bobbym
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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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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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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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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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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

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

Compute Sin[.1]


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

anonimnystefy
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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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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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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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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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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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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
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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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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
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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
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Registered: 2011-05-23
Posts: 15,544

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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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

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

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
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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

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

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
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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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

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

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
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,219

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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