# Investigate the validity of Taylor's theorem for f

• November 17th 2009, 10:06 PM
dabien
Investigate the validity of Taylor's theorem for f
f(x) = x^2 sin (1/x) if x in (-1,1) and x is not 0
f(x)=0 if x=0
Investigate the validity of Taylor's theorem for f about the point x=0
• November 18th 2009, 11:13 PM
chisigma
An $f(x)$ can be expanded in Taylor series around $x=x_{0}$ if in that point $f(x)$ and all its derivatives do exist. For the function You have proposed, in $x=0$, $f(x)$ does exist but $f^{'}(x)$ doesn't (Shake) ...

Kind regards

$\chi$ $\sigma$