Re: Strange result of Limit function in Mathematica3.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg16034] Re: [mg15987] Strange result of Limit function in Mathematica3.0*From*: BobHanlon at aol.com*Date*: Sat, 20 Feb 1999 02:52:14 -0500*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2/19/99 1:45:56 PM, krupa at alpha.sggw.waw.pl writes: >It is well known that: >(2^n+8^n)^(1/n)->8 as n->Infinity >and >(2^n+3^n)^(1/n)->3 as n->Infinity > >but mathematica3.0 gives very strange results: > > >In[1]:=<<Calculus`Limit` > >In[2]:= Limit[(2^n+8^n)^(1/n),n->Infinity] > >Out[2]:= 1/E > > >In[3]:=Limit[(2^n+3^n)^(1/n),n->Infinity] > >Out[3]:= E > >Does Mathematica3.0 give such strange results only >on my machine or may be I have made some mistake? > Jan, Needs["Calculus`Limit`"] Limit sometimes needs help. If you simplify the form of the expression prior to using Limit you will get the results which you expected. 8*Limit[((1/4)^n + 1)^(1/n), n -> Infinity] 8 3*Limit[((2/3)^n + 1)^(1/n), n -> Infinity] 3 In any case, always do a sanity check of the results from Limit. Table[(2^n + 8^n)^(1/n), {n, 6, 10}]//N {8.00033,8.00007,8.00002,8.,8.} Table[(2^n + 3^n)^(1/n), {n, 22, 26}]//N {3.00002,3.00001,3.00001,3.,3.} Bob Hanlon