Re: Very simple limit, why doesn't it evaluate?

*To*: mathgroup at smc.vnet.net*Subject*: [mg31923] Re: [mg31909] Very simple limit, why doesn't it evaluate?*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>*Date*: Wed, 12 Dec 2001 04:14:04 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Computing limits is done by means of a number of ad hoc tricks rather than a universal algorithm, so there will always be cases that Mathematica can't manage but can be done "by hand". In general when Mathematica can't find a limit it is a good idea to load in the Calculus`Limit` package and try again. In this case this case we get: << Calculus`Limit` In[2]:= Limit[4^(3 + n)/(-5 + 3^(4 + n)), n -> Infinity] Out[2]= Infinity This is with Mathematica 4.1 so I am not sure what happens with 3.0 but I suspect the same thing. Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Tuesday, December 11, 2001, at 03:33 PM, Jacek Dziedzic wrote: > It stunned me that the Mathematica 3.0 returns this very simple limit > unevaluated: > 4^(n+3)/(3^(n+4)-5), with n -> infinity. > > Moreover, the NLimit function returns 1.0756... which is a rather poor > approximation of infinity (the expected result)... Well I can understand > that NLimit is numerical and can't be relied on, but why does the > original > Limit[] die on that? Or am I doing anything wrong? > > - Jacek Dziedzic > > > > >