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MathGroup Archive 2005

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Re: Why are the functions different?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55663] Re: Why are the functions different?
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Fri, 1 Apr 2005 05:37:14 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/31/05 at 1:24 AM, helge.stenstrom.NOSPAM at NOSPAMericsson.com
(Helge Stenstroem) wrote:

>How are these two functions (f0 and f1) different? f0 can be
>plotted, but f1 cannot.

>f1[x_] := Normal[Series[Tanh[x], {x, 0, 5}]] 
>f0[x_] := x - x^3/3 +(2*x^5)/15

>When evaluated like this:
>f0[x] 
>f1[x]
>they look the same.

>The following gives error messages if f0 is replaced by f1.
>Plot[{Tanh[z], f0[z]}, {z, -1, 1}]

The problem is evaluation with a numeric argument. If you supply f1 with a numeric argument, Tanh evaluates to a number and the arguements to Series will not be valid.

This can be fixed by using Set instead of SetDelayed in the definition of f1, i.e.,

f1[x_] = Normal[Series[Tanh[x], {x, 0, 5}]]

With this definition, the rhs gets evaluated to x - x^3/3 +(2*x^5)/15 before any number is supplied to f1 and f1[x] will evaluate to a number when x is a number as Plot requires.
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