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MathGroup Archive 2004

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RE: Graphs of Sequences of Functions:(

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46905] RE: [mg46900] Graphs of Sequences of Functions:(
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sun, 14 Mar 2004 23:54:22 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Eleanna,

How about...

Needs["Graphics`Colors`"]

Plot[Evaluate[Table[x^n, {n, 0, 10}]], {x, 0, 1},
    PlotRange -> All,
    Frame -> True,
    FrameLabel -> {x, f},
    RotateLabel -> False,
    PlotLabel -> SequenceForm[f == x^n, " as n goes from 0 to 10"],
    Background -> Linen,
    ImageSize -> 450];

We make a table of the functions. The Table has to be evaluated in the Plot
statement for the Plot statement to work correctly. PlotRange -> All is
necessary else Mathematica just shows what it thinks is the "interesting
part".

We obtain a better representation by using an uneven set of integers for n.
How do we do that with a Table? We can't but we can do it with MapThread.
For example...

MapThread[x^#&,{{0, 1, 2, 3, 5, 10, 20, 50, 100}}]
{1, x, x^2, x^3, x^5, x^10, x^20, x^50, x^100}

MapThread is a way to make a table with arbitrary values. x^#& is a pure
function. Then the following gives a more indicative plot.

Plot[Evaluate[MapThread[x^# &, {{0, 1, 2, 3, 5, 10, 20, 50, 100}}]], {x, 0,
      1},
    PlotRange -> All,
    Frame -> True,
    FrameLabel -> {x, f},
    RotateLabel -> False,
    PlotLabel -> SequenceForm[f == x^n, " for increasing n from 0 to 100"],
    Background -> Linen,
    ImageSize -> 450];


David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/




From: Eleanna Tsoumani [mailto:eleanna_tsoumani at yahoo.gr]
To: mathgroup at smc.vnet.net

Hi all,

I am trying to do the graphs of some sequences of functions,using
mathematica 4.0, in order to see if their convergence is uniform or not.

For example : Fn(x) = x^n , 0=< x =<1.

The problem is that the graphs have to be 2D (not 3D) but I cannot
find a way to do that.  Any suggestions?
THANK YOU!

Eleanna




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