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MathGroup Archive 1991

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Re: Funny Limits

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Funny Limits
  • From: Jack Seltzer <jack at chopin.udel.edu>
  • Date: Mon, 30 Sep 91 10:33:07 -0400

>From stevec at yoda.physics.unc.edu Sat Sep 28 05:53:47 1991
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>Message-Id: <9109280339.AA09904 at yoda.physics.unc.edu>
>Date: Wed, 25 Sep 91 10:49:45 PDT
>From: Steve Trainoff <steve at tweedledee.ucsb.edu>
>To: mathgroup at yoda.physics.unc.edu
>Subject: Funny Limits
>Status: RO
>
>Hello all,
>
>I just got my new copy of MMA 2.0 and have been playing around with it.  It appears  
>to have some annoying "features."  I had hoped that the Limit function would be more  
>robust under 2.0.  Not so.  Here is an example.  I always thought that the limit of  
>x^n/E^x as x->Infinity was zero or all values of n.  MMA apparantly thinks  
>otherwise, moreover it appears that MMA 2.0 has less persistance than MMA 1.
>Notice that MMA 1.2 got farther than 2.0 and also gave a warning method that it  
>couldn't find the answer when it gave up.  MMA 2.0 just quit silently.
>
>...STeve
>
>Example 1:
>------------------------------------------------------------
>Mathematica (NeXT) 1.2 (January 20, 1990) [With pre-loaded data]
>by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin,
>   S. Omohundro, D. Ballman and J. Keiper
>with I. Rivin and D. Withoff
>Copyright 1988,1989,1990 Wolfram Research Inc.
>
>In[1]:= Table[Limit[x^n/E^x, x->Infinity], {n, 0, 15}]   
>
>
>Limit::nlm: Could not find definite limit.
>
>Limit::nlm: Could not find definite limit.
>
>Limit::nlm: Could not find definite limit.
>
>General::stop: Further output of Limit::nlm
>     will be suppressed during this calculation.
>
>                                                       13
>                                                      x
>Out[1]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, Limit[---, x -> Infinity], 
>
>                                                       x
>                                                      E
> 
>
>            14                         15
>           x                          x
>>    Limit[---, x -> Infinity], Limit[---, x -> Infinity]}


(rest of msg deleted)

The problem above is the order of evaluation...using Release eliminates the
difficulty as shown below...

In[15]:=  Table[Release[Limit[x^n/E^x,x->Infinity]],{n,0,30}]

Out[15]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

>    0, 0, 0, 0, 0, 0, 0, 0, 0}






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