Limit computed incorrectly
- To: mathgroup at smc.vnet.net
- Subject: [mg103274] Limit computed incorrectly
- From: Adam Weyhaupt <aweyhau at siue.edu>
- Date: Sat, 12 Sep 2009 07:26:09 -0400 (EDT)
A colleague recently pointed out the following incorrect calculation of a limit in Mathematica 7.0.1 on Mac OS X 10.4.11 (this occurs on Windows as well, but this limit is calculated correctly in Mathematica 6). In[1]:= Clear[k, x] (* the next two limits should be equal *) In[2]:= Limit[1 + k Sqrt[2 x ] + k x, x -> 3.1] Out[2]= 1. + 0.61002 k In[3]:= 1 + Limit[ k Sqrt[2 x ] + k x, x -> 3.1] Out[3]= 1 + 5.58998 k In[4]:= Limit[1 + k Sqrt[2 x ] + k x, x -> 31/10] Out[4]= 1 + (31/10 + Sqrt[31/5]) k In[5]:= 1 + Limit[ k Sqrt[2 x ] + k x, x -> 31/10] Out[5]= 1 + 1/10 (31 + 2 Sqrt[155]) k In[6]:= Simplify[% - %%] Out[6]= 0 What's going on? Is this a case of "don't mix symbolic and numeric computation"? I'm surprised to get a problem near 3.1, since we don't seem to be near any obvious singularities. Thanks, Adam