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

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- Nov 17th 2009, 10:06 PMdabienInvestigate 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 - Nov 18th 2009, 11:13 PMchisigma
An $\displaystyle f(x)$ can be expanded in Taylor series around $\displaystyle x=x_{0}$ if in that point $\displaystyle f(x)$ and all its derivatives do exist. For the function You have proposed, in $\displaystyle x=0$, $\displaystyle f(x)$ does exist but $\displaystyle f^{'}(x)$ doesn't (Shake) ...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$