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MathGroup Archive 1999

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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


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