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