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