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MathGroup Archive 2005

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Re: Strange "little" problem with scaling

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62676] Re: [mg62659] Strange "little" problem with scaling
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 30 Nov 2005 22:08:38 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

The Plots are correct.  They should have different shapes.  Perhaps you are 
being misled by looking at the plots on different scales, with different origins. 
Plot them together.

y1[x_]:=(Sin[x]-x*Cos[x])/x^3;
y2[x_]:=y1[x]/2;
Plot[y1[x],{x,0,Pi}];
Plot[y2[x],{x,0,Pi}];
Plot[{y1[x],y2[x]},{x,0,Pi},Epilog->{Red,AbsolutePointSize[4],
        Point/@{{Pi,1/Pi^2},{Pi,1/2/Pi^2}}}];


Bob Hanlon

> 
> From: "Srinath  Avadhanula" <srinathava at gmail.com>
To: mathgroup at smc.vnet.net
> Date: 2005/11/30 Wed AM 12:08:11 EST
> Subject: [mg62676] [mg62659] Strange "little" problem with scaling
> 
> Hi all,
> 
> I have an absurd little problem which unfortunately, I am unable to
> figure out the solution to... Consider the following very simple
> notebook:
> 
> \!\(y1[x_] := \(Sin[x] - x\ Cos[x]\)\/x\^3\[IndentingNewLine]
>   y2[x_] := \(1\/2\) y1[x]\[IndentingNewLine]
>   Plot[{y1[x]}, \ {x, \ 0, \ p}]\[IndentingNewLine]
>   Plot[{y2[x]}, \ {x, \ 0, \ p}]\)
> 
> The above can be copied/pasted into a new mathematica notebook. If you
> do not wish to do this, please see a screenshot at:
> 
> http://robotics.eecs.berkeley.edu/~srinath/mathematica_prob.png
> 
> Basically, I have defined two functions y1[x] and y2[x] which _should_
> ideally only differ by a factor of 2. However, their shapes when I plot
> them are _completely_ different! I simply do not understand what I am
> doing wrong. I am pretty sure that this is a syntax issue with the way
> I am defining the various functions.
> 
> Thinking a little bit more about this, it looks like neither of the two
> plots are correct! The correct value of y1[pi] == 1/pi^2 and y2[pi] ==
> 1/2/pi^2. It doesn't look like the plots are anywhere close to this.
> 
> My Mathematica version: 5.1
> 
> Many thanks for any help (I apologize in advance for this silliness)
> Srinath
> 
> 


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