Table of contents |

2 How it is ill-behaved 3 How this is negatively a good thing 4 How this is positively a good thing |

Consider the real function

One can show that *f* has derivatives of all orders at every point including 0. To show this at *x* = 0, use L'Hopital's rule, mathematical induction, and some simple substitutions.

[*Detail could be put here.*]

But in proving this, one will find that *f*^{(n)}(0) = 0 for all *n*. Therefore, the Taylor series of *f* is