Oh,Oh,Oh,merry analysis!!!

anonimnystefy · 2012-01-21 07:48:39

hi bobbym

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

bobbym · 2012-01-21 07:52:34

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

anonimnystefy · 2012-01-21 07:53:30

ok.next?

bobbym · 2012-01-21 07:55:21

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

anonimnystefy · 2012-01-21 08:01:33

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.

bobbym · 2012-01-21 08:04:17

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

anonimnystefy · 2012-01-21 08:04:51

me neither.

bobbym · 2012-01-21 08:07:03

Compute Sin[.1]

anonimnystefy · 2012-01-21 08:12:08

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?

bobbym · 2012-01-21 08:12:59

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

anonimnystefy · 2012-01-21 08:14:25

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)

John E. Franklin · 2012-01-21 08:14:26

Use radians?

bobbym · 2012-01-21 08:21:01

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.

anonimnystefy · 2012-01-21 08:23:32

hi bobbym

i forgot a zero by accident.fixed it now.

bobbym · 2012-01-21 08:26:50

You will need more decimal places for this example.

anonimnystefy · 2012-01-21 08:29:26

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

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

bobbym · 2012-01-21 08:30:45

Now compute using that series the value .1

anonimnystefy · 2012-01-21 08:36:19

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)

bobbym · 2012-01-21 21:22:19

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?

anonimnystefy · 2012-01-22 01:50:46

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.

bobbym · 2012-01-22 02:04:57

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

anonimnystefy · 2012-01-22 02:09:24

hi bobbym

next one please.

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

bobbym · 2012-01-22 02:19:53

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

anonimnystefy · 2012-01-22 02:22:46

hi bobbym

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

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

bobbym · 2012-01-22 02:30:32

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?

Math Is Fun Forum

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

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

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

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

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

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

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

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

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

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

#31 2012-01-21 08:04:17

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

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

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#33 2012-01-21 08:07:03

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

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

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#35 2012-01-21 08:12:59

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

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

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#37 2012-01-21 08:14:26

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

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

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#40 2012-01-21 08:26:50

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

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

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#42 2012-01-21 08:30:45

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

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

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#44 2012-01-21 21:22:19

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

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

#46 2012-01-22 02:04:57

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

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

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

#48 2012-01-22 02:19:53

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

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

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#50 2012-01-22 02:30:32

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

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