From: utzoo!decvax!harpo!npoiv!alice!rabbit!ark Newsgroups: net.misc Title: Re: Using Taylor Series To Extrapolate Article-I.D.: rabbit.649 Posted: Sat Jul 31 22:29:26 1982 Received: Sun Aug 1 03:25:32 1982 References: eagle.435 It is indeed true that you can extrapolate the behavior of a function everywhere from its behavior at a single point, provided that (a) "behavior" means "value of the function and all its derivatives," and (b) the function and all its derivatives are continuous (and, by implication, differentiable) everywhere.