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Function Programming Problems

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90782] Function Programming Problems
  • From: davey79 at gmail.com
  • Date: Thu, 24 Jul 2008 04:51:59 -0400 (EDT)

Hello,

A colleague and myself are working on some Mathematica labs for
Calculus using Mathematica 6.0 and I can't seem to find any
information or examples that explain defining functions and using
functions as arguments.

I want to define a LinearApproximation command that preferably would
take two arguments and return the linear approximation.  Ideally,

LinearApproximation[function_,a_] would have
LinearApproximation[Sin[x],0] give "x" as the output.

So far I have:
LinearApproximation[function_, a_, x_] := function[a] +
function'[a]*(x - a)

which works mostly nicely, except it only works with
LinearApproximation[Sin,0,x].

Does anyone know how I would fix this to allow Sin[x] as input (or
even x^2, etc)?  Getting rid of the third argument "x" would be nice,
but not necessary.

Thanks!

David Taylor
Roanoke College


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