       Re: Function Programming Problems

• To: mathgroup at smc.vnet.net
• Subject: [mg90825] Re: [mg90782] Function Programming Problems
• Date: Fri, 25 Jul 2008 06:17:08 -0400 (EDT)
• References: <200807240851.EAA18893@smc.vnet.net>

```David,

1.

In:= LinearApproximation[f_, x0_, x_] := (f /. {x -> x0}) +  (D[f, x] /.
{x -> x0})*(x - x0);

LinearApproximation[Sin[x], Pi/4, x]

Out= 1/Sqrt + (-(Pi/4) + x)/Sqrt

2.

In:= LinearApproximation1[f_, x0_, x_] := Normal[Series[f, {x, x0,
1}]];

LinearApproximation1[Sin[x], Pi/4, x]

Out= 1/Sqrt + (-(Pi/4) + x)/Sqrt

3.

In:= LinearApproximation2[f_, x0_, x_, n_] := Normal[Series[f, {x, x0,
n}]];

LinearApproximation2[Sin[x], Pi/4, x, 5]

Out= 1/Sqrt + (-(Pi/4) + x)/Sqrt - (-(Pi/4) + x)^2/(2*Sqrt) -
(-(Pi/4) + x)^3/(6*Sqrt) + (-(Pi/4) + x)^4/(24*Sqrt) +
(-(Pi/4) + x)^5/(120*Sqrt)

2008/7/24 <davey79 at gmail.com>:

> 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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