Basic Analysis I — Real Analysis · Problem 4.3.5

The Derivative — Jiri Lebl

Mathematics — Real Analysis · taylor-remainder-limit

Problem

f : [a,b] \to \mathbb{R}

has

n+1

continuous derivatives and

x_0 \in [a,b]

, prove

\displaystyle\lim_{x \to x_0} \frac{R_n^{x_0}(x)}{(x - x_0)^n} = 0