Example 8-5-1 - Maple Help



Chapter 8: Infinite Sequences and Series



Section 8.5: Taylor Series

Example 8.5.1



 Show that the formal Maclaurin expansion of $f\left(x\right)=\left\{\begin{array}{cc}{e}^{-1/{x}^{2}}& x\ne 0\\ 0& x=0\end{array}\right\$is identically zero, so that this expansion does not represent $f\left(x\right)$. Hint: Show that ${f}^{\left(n\right)}\left(0\right)=0$ for $n=1,2,\dots$.







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