Залишковий член у формі Лагранжа

If $T_n(x)$ is the degree $n$ Taylor approximation of $f(x)$ at $x=a$, then the approximation error $R_n(x) = f(x) - T_n(x)$ (sometimes called remainder), in Lagrange mean-value form, is $$R_n(x) = \frac{f^{(n+1)}(\xi_L)}{(n+1)!} (x-a)^{n+1}$$ for some real number $\xi_L$ strictly between $a$ and $x$. (Technical hypotheses: this formula holds if $f^{(n)}$ is continuous on the closed interval between $a$ and $x$, and differentiable on the open interval between $a$ and $x$.)