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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



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