       Re: Function Programming Problems

• To: mathgroup at smc.vnet.net
• Subject: [mg90835] Re: [mg90782] Function Programming Problems
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 25 Jul 2008 06:19:04 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```Clear[linearApproximation];

linearApproximation[expr_, a_, x_Symbol: x] :=
Module[{var},
(expr + D[expr, x]*(var - a)) /.
{x -> a, var -> x}];

linearApproximation[Sin[a*x], 0] ==

Series[Sin[a*x], {x, 0, 1}] // Normal

True

linearApproximation[Exp[-a*x], 0] ==

Series[Exp[-a*x], {x, 0, 1}] // Normal

True

linearApproximation[f[y], a, y] ==

Series[f[y], {y, a, 1}] // Normal

True

Bob Hanlon

---- 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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