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Re: Function Programming Problems

On Jul 24, 2008, at 4:51 AM, davey79 at wrote:

> 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.

Sin[x] is not a function  in Mathematica, Sin[#]& or Function[{x},Sin 
[x]] are functions, you can pass them as arguments, so


works, as does


Two other notes; first Mathematica will simplify the resulting  
polynomials so you may not get the exact results you expected,  
secondly for built in functions of a single argument the expression

LinearApproximation[Sin, a, x]

is also allowed as shorthand.

Finally, Mathematica already has a function for series expansion  
called Series which you may want to look at.



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