computing derivatives and limits

*To*: mathgroup at smc.vnet.net*Subject*: [mg126020] computing derivatives and limits*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Fri, 13 Apr 2012 04:47:48 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Consider the function: f[x_] := Cos[Sqrt[x]] This is an analytic function and of course Mathematica knows its Taylor series: SeriesCoefficient[f[x], {x, 0, n}] Piecewise[{{(-1)^n/(2*n)!, n >= 0}}, 0] But asking for the derivative at 0 is asking for trouble: f'[0] During evaluation of In[203]:= Power::infy: Infinite expression 1/Sqrt[0] encountered. >> During evaluation of In[203]:= Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered. >> Indeterminate This is, in fact, taken from a question that appeared at our recent calculus test and those who gave the same answer as Mathematica got 0 points for it. I understand why this happens but shouldn't Mathematica be a little cleverer about this sort of thing nowadays, particularly in situations when it can find the Taylor series? Andrzej Kozlowski