How Does o-Notation Affect Operations in Taylor Series Expansions?

[transgalactic]

i know that the in the remainder is x^5

but till what power i open the expression??

what happanes when i multiply to expression of o(x^4) in one of them
and o(x^5) in the other

or when we are making a sun of these two expressions

 

[arildno]

I some expression f(x) is o(x^n), it means that
$$\lim_{x\to{0}}\frac{f(x)}{x^{n}}=0$$

 

[transgalactic]

i ment in a tailor series

 

[transgalactic]

what are the laws of making operation with taylor serieses regarding the o(x^n) object