       Re: Function Programming Problems

• To: mathgroup at smc.vnet.net
• Subject: [mg90807] Re: Function Programming Problems
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 25 Jul 2008 06:12:21 -0400 (EDT)
• References: <g69fqt\$ie1\$1@smc.vnet.net>

```Hi,

if you say:

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

you have to give a pure function and

LinearApproximation[#^2 &, 0, x] will work

For a general expression you have to give a symbol
where the expression depend on, i.e. add a rule:

LinearApproximation[foo_,y_,at_,x_]:=LinearApproximation[Function[{y},foo],at,x]

Regards
Jens

davey79 at gmail.com 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.
>
> Thanks!
>
> David Taylor
> Roanoke College
>

```

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