You are not logged in.
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
Offline
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.
Offline
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
Offline
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.
Offline
if i'm not wrong that's the approximation of the sin(x) function.
well it means that sin(x)x+x^3/6x^5/120<c*x^6 for some const. c>0
i expect the value of xx^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
Offline
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.
Offline
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
Offline
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.
Offline
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
Offline
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.
Offline
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 (20120121 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
Offline
Use radians?
igloo myrtilles fourmis
Offline
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.
Offline
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
Offline
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.
Offline
ok then.can do. 0.0998334.i think it's enough.
Last edited by anonimnystefy (20120121 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
Offline
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.
Offline
0.0998334...the same
i used alpha.it says the difference is about 2*10^(11)
Last edited by anonimnystefy (20120121 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
Offline
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.
Offline
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
Offline
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.
Offline
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
Offline
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.
Offline
hi bobbym
Last edited by anonimnystefy (20120122 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
Offline
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.
Offline