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MathGroup Archive 1991

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Re: Funny Limits

  • To: mathgroup at yoda.physics.unc.edu, bugs
  • Subject: Re: Funny Limits
  • From: Steve Trainoff <steve at tweedledee.ucsb.edu>
  • Date: Mon, 30 Sep 91 11:08:52 PDT

I wrote a message about problems with evaluating the limit:
Table[Limit[x^n/E^x, x->Infinity], {n, 0, 15}]

> To which I got the reply from From: Jack Seltzer <jack at chopin.udel.edu>
> 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}
> 

> 


This indeed works under MMA 1.2 but not under MMA 2.0. I get:

Mathematica 2.0 for NeXT
Copyright 1988-91 Wolfram Research, Inc.
 -- NeXT graphics initialized -- 


In[1]:= Table[Release[Limit[x^n/E^x,x->Infinity]],{n,0,5}]

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


The real problem I wanted I had was with the limit,

Limit[x^n/E^x, x->Infinity]

for an UNSPECIFIED n.  With Jack's suggestion MMA 1.2
correctly evaluates this as:
-----------------------------
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]:= Release[Limit[x^n/E^x, x->Infinity]]

Out[1]= 0

whereas MMA 2.0 yields:
-----------------------------
Mathematica 2.0 for NeXT
Copyright 1988-91 Wolfram Research, Inc.
 -- NeXT graphics initialized -- 


In[1]:= Release[Limit[x^n/E^x, x->Infinity]]

               n
              x
Out[1]= Limit[--, x -> Infinity]
               x
              E

...STeve
------------------------------------
Insert pithy maxim here...
steve at tweedledee.ucsb.edu (NeXT mail)





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