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#26 2012-01-22 06:48:39

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

hi bobbym

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#27 2012-01-22 06:52:34

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#28 2012-01-22 06:53:30

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

ok.next?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#29 2012-01-22 06:55:21

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#30 2012-01-22 07:01:33

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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#31 2012-01-22 07:04:17

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#32 2012-01-22 07:04:51

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

me neither.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#33 2012-01-22 07:07:03

bobbym

Online

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

Compute Sin[.1]

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#34 2012-01-22 07:12:08

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?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#35 2012-01-22 07:12:59

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#36 2012-01-22 07:14:25

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 (2012-01-22 07:23:08)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#37 2012-01-22 07:14:26

John E. Franklin
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Re: Oh,Oh,Oh,merry analysis!!!

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

#38 2012-01-22 07:21:01

bobbym

Online

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;

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#39 2012-01-22 07:23:32

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

hi bobbym

i forgot a zero by accident.fixed it now.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#40 2012-01-22 07:26:50

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#41 2012-01-22 07:29:26

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 (2012-01-22 07:29:37)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#42 2012-01-22 07:30:45

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#43 2012-01-22 07:36:19

anonimnystefy
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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 (2012-01-22 07:36:38)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#44 2012-01-22 20:22:19

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#45 2012-01-23 00:50:46

anonimnystefy
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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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#46 2012-01-23 01:04:57

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#47 2012-01-23 01:09:24

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

hi bobbym

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#48 2012-01-23 01:19:53

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#49 2012-01-23 01:22:46

anonimnystefy
Real Member

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

hi bobbym

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

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#50 2012-01-23 01:30:32

bobbym

Online

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.