EDB — 1NC

[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 $\sqrt{1+x_0^2}$.

Study similarly $f(x)=\sqrt{x^2+1}$ or $f(x)=e^{1/(x^2+1)}$.