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Re: Re: Re: The graph of (x + 2)^(1/5) + 4 not

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103989] Re: [mg103938] Re: [mg103926] Re: The graph of (x + 2)^(1/5) + 4 not
  • From: victor chg <kindlychung at gmail.com>
  • Date: Wed, 14 Oct 2009 07:58:49 -0400 (EDT)
  • References: <868306d90910120643u7f1c2299v2cd1845508dc85b7@mail.gmail.com>

Here is the correct link:
http://i35.tinypic.com/11jrtpk.jpg

On Wed, Oct 14, 2009 at 11:17 AM, Murray Eisenberg <murray at math.umass.edu>wrote:

> Could you please just tell us what you think is wrong with the plot that
> Mathematica provides?
>
> I ask because when I point my browser to the link you provide...
>
> (1) I get a large number of annoying (and potentially dangerous)
> 3rd-party ad-generating items on the URL page that clamor to be allowed
> to do their thing.
>
> (2) The plot finally displayed is of something entirely different -- of
> exp(-x^2) and its first two derivatives.
>
> As to the function (x + 2)^(1/5) + 4 that you asked about: Did you just
> try something like the following?
>
>   Plot[(x + 2)^(1/5) + 4, {x,-7,5}]
>
> If so, then you were probably surprised that the graph ended on the left
> at x == -2.  And that is precisely what Mathematica should be expected
> to do. After all, Mathematica "wants" numbers to be complex when they
> can be.  And z^(1/5) denotes the PRINCIPAL 5th-root of z, so that when z
> is negative, you do NOT get a negative real number, but rather the
> non-real, complex principal 5th-root.
>
> If you want the high school/calculus variety 5th-root function, then you
> need to finesse this. For example:
>
>   f[x_] := Sign[x + 2] Abs[x + 2]^(1/5) + 4
>   Plot[ f[x], {x,-7,5}]
>
> (You could use Piecewise instead.)
>
> victor chg wrote:
> > Here is the link to the image:
> > http://tinypic.com/view.php?pic=veae6u&s=4
> >
> > Victor Chg
>
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305
>
>


-- 
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Neuroscience Research Institute, Peking University, Beijing, P.R.China
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