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 $n\rightarrow \infty$