Setting You can observe that is...
Now if is...
... the (1) becomes...
... and from (3) You derive...
... so that is...
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.
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 .