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 >Received: from yoda.physics.unc.edu by brahms.udel.edu with SMTP > (5.61+/IDA-1.2.8) id AA13640; Sat, 28 Sep 91 05:53:45 -0400 >Received: by yoda.physics.unc.edu (4.0/TAS/11-16-88) > id AA09908; Fri, 27 Sep 91 22:39:32 CDT >Received: by yoda.physics.unc.edu (4.0/TAS/11-16-88) > id AA09904; Fri, 27 Sep 91 22:39:31 CDT >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}