Solution
= Solution
Choose a compact interval around $x_0$ and its constant $C$. For $|h|\lt 1/C$, the Lagrange remainder after order $n$ is at most $(C|h|)^{n+1}\to0$. Thus the <taylor series> with $a_n=f^{(n)}(x_0)/n!$ equals $f(x_0+h)$.
= Solution
Choose a compact interval around $x_0$ and its constant $C$. For $|h|\lt 1/C$, the Lagrange remainder after order $n$ is at most $(C|h|)^{n+1}\to0$. Thus the <taylor series> with $a_n=f^{(n)}(x_0)/n!$ equals $f(x_0+h)$.