It bugs me when students assume that *f*(*x*) and its Taylor series are always the same.
They aren't, of course. A simple counter-example is . The
Taylor series at 1 is 1+(*x*-1), with the rest of the terms equal to zero. But
this sums to *x*, which does not equal *f*(*x*) for negative *x*'s.

Mon May 5 12:53:33 CDT 1997