[1NC]Prerequisites:[1KQ]↺↻.
Show that \(f(x)=\frac 1{1+x^ 2}\) is analytic on all \(ℝ\), but the radius of convergence of the Taylor seried centered in \(x_ 0\) is \(\sqrt{1+x_ 0^ 2}\).
[1ND]↺↻
Study similarly \(f(x)=\sqrt{x^ 2+1}\) or \(f(x)=e^{1/(x^ 2+1)}\).
