Let $f$ be a function which is defined on the interval$(a,b)$ and suppose the $n$derivative$f^{(n)}$ exists on $(a,b)$ Then for all $x$ and $x_0$ in $(a,b)$
$$ R_n(x) = \frac{f^{(n)}(y)}{n!}(x-x_0)^n $$
with $y$strictly between $x$ and $x_0$ ($y$ depends on the choice of $x$ . $R_n(x)$ is the $n$remainder of the Taylor series for $f(x)$
