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MathGroup Archive 1991

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Funny Limits

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Funny Limits
  • From: Steve Trainoff <steve at tweedledee.ucsb.edu>
  • Date: Wed, 25 Sep 91 10:49:45 PDT

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]}
            x                          x
---------------------------------------------------------
Example 2:
Mathematica 2.0 for NeXT
Copyright 1988-91 Wolfram Research, Inc.
 -- NeXT graphics initialized -- 


In[1]:= Table[Limit[x^n/E^x, x->Infinity], {n, 0, 6}] 


                            4                         5
                           x                         x
Out[1]= {0, 0, 0, 0, Limit[--, x -> Infinity], Limit[--, x -> Infinity], 

                            x                         x
                           E                         E
 

            6
           x
>    Limit[--, x -> Infinity]}
            x
           E

--------------------------------------------------------





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