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A function which doesn't equal its Taylor series, part 1

It bugs me when students assume that f(x) and its Taylor series tex2html_wrap_inline431 are always the same. They aren't, of course. A simple counter-example is tex2html_wrap_inline433 . 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.

Tom Vogel
Mon May 5 12:53:33 CDT 1997