Remainder of the taylor expansion as a function of the dimension of the space

Given a function $f(x):\mathbb R^n \rightarrow \mathbb R$ under certain conditions it can be approximated with the Taylor expansion: $f(x) = p(x) + r$ where $p$ is a polynomial and $r$ is the remainder. I would like to know if there is a formula for $r$ where is present the dimension of the space $n$.

In particular I am curios to know if the reminder goes to 0 when $n\rightarrow \infty$

• Have a look at en.wikipedia.org/wiki/Taylor's_theorem hope it helps! – Klaramun Dec 4 '14 at 16:43
• I'll check again but I think that there is not reported the reminder in for $n>1$ – Donbeo Dec 4 '14 at 16:49
• I think it is, see the section "Taylor's theorem for multivariate functions" – Klaramun Dec 4 '14 at 16:51
• yes you are right it is there but it is not a function of $n$. I am curios to know if there is another expression where $n$ is relevant. – Donbeo Dec 4 '14 at 16:53