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MathGroup Archive 2005

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Re: Strange "little" problem with scaling

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62665] Re: Strange "little" problem with scaling
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Wed, 30 Nov 2005 05:40:38 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/30/05 at 12:08 AM, srinathava at gmail.com (Srinath  Avadhanula)
wrote:

>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
>y2[x_] := (1/2)*y1[x]

>Plot[{y1[x]}, {x, 0, Pi}]
>Plot[{y2[x]}, {x, 0, Pi}]

<changed to input form for better readability>

>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.

You've done nothing wrong as far as I can see. But you assumption that the shapes should look the same isn't correct. Consider, both functions have zeros at identical points. Additionally, the peak value of one function is twice that of the other. So, the one function that is half of the other will appear flatter. That is for non-linear functions a change of scale on one axis is not generally a shape preserving transform.
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