Setting You can observe that is...
(1)
Now if is...
(2)
... the (1) becomes...
(3)
... and from (3) You derive...
... so that is...
(4)
Kind regards
determine Maclaurin development of order 3 with residual term with o notation e^sinx
My main problem is that i don't understand the rules of O notation
1. e^sinx ... u= sinx
we get e^u
2. Develeopment of e^x = 1 + x + x^2/2 + (O(x^4))
Develeopment of sinx = x - 1/6 x^3 + O(x^5)
3. e^sinx = e^x-x^3/6 * e^(O(x^5))
= e^x * e^-x^3/6 * e(O(x^5))
I could need some help finish this off
secondly I don't understand why we put an O notation of O(x^5)) here out of a sudden, we had an ordo of 4 as well didnt we?
Would be grateful if someone could explain all the Ordo (O notation) rules so that i can start working on problem self without using hints like the one above. All that we have is a booklet handout with problems + a very bad book that does not cover the topic well.
Thanks alot
Setting You can observe that is...
(1)
Now if is...
(2)
... the (1) becomes...
(3)
... and from (3) You derive...
... so that is...
(4)
Kind regards
Incase the OP was wondering the MEANING of the "Big Oh" notation, to use what so kindly posted...
The in this example means that when you are evaluating this function for values close to (as you would with a MacLaurin Series - if not, you would use a Taylor Series centred around a point closer to the point you are evaluating the function at), the absolute error (remainder) is no greater than some constant multiple of .