       • To: mathgroup at smc.vnet.net
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Tue, 11 Feb 2003 04:42:14 -0500 (EST)
• References: <b27ft7\$nel\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Baruch,
The basic problem is that Plot decides what kind of expression {t} is before
evaluating {t}. In this case it decides that Flatten[{t}] must be a list of
one  real number for the sample values of x that it uses. This is not so, in
fact Flatten[{t}] becomes a list of several real numbers.
We can supply Plot with information to make the correct decision by causing
{t} to evaluate before is makes its decision ( I have included f[x] in the
plot, and used df = f'  (note =, not :=) to avoid evluating f' at each
iteration).
You might like to consider avoiding the use of  Plot  for the tangent lines
by adding fo each approximation,a,  Line[{a,f[a]},{b,0}] where {b,0} is
where the tangent at  a  meets the x-axis -- Epilog might be used.

f[x_] := x^2 - 2
Ne[x_] := x - f[x]/f'[x]
ap = NestList[Ne, 4., 5]
tang[h_] := f[h] + f'[h]*(x - h)
t = tang /@ ap

Plot[Evaluate[Prepend[t, f[x]]], {x, -5, 5},
AxesOrigin -> {0, 0}, PlotRange -> {-3, f}]

Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"baruch" <spin9 at terra.com.br> wrote in message
news:b27ft7\$nel\$1 at smc.vnet.net...
> f[x_] := x^2 - 2
> Ne[x_] := x - f[x]/f'[x]
> ap = NestList[Ne, 1.5, 5]
> tang[h_] := f[h] + f'[h](x - h)
> t = tang /@ ap
>
> Plot[{t}, {x, -10, 10}, AxesOrigin -> {0, 0},
>   PlotRange -> {{-5, 5}, {-3, 5}}]
>
> Now, How can I plot the last command?
>
> I got the following errors:
>
> Plot::"plnr": "\!\(te[x]\) is not a machine-size real number at
> \!\(x\) = \
> \!\(-9.999999166666667`\)."
> Plot::"plnr": "\!\(te[x]\) is not a machine-size real number at
> \!\(x\) = \
> \!\(-9.188660168541684`\)."
>
> I want to make a "program" that will plot the successives tangent
> lines of approximations of any function (when possible) using the
> Newton Methods... any idea on how can I implement or solve that
> problem?
>
> Thank you very much!
>

```

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