Re: Bug in Limit ?
- To: mathgroup at smc.vnet.net
- Subject: [mg25991] Re: [mg25951] Bug in Limit ?
- From: BobHanlon at aol.com
- Date: Wed, 15 Nov 2000 02:09:42 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 11/14/00 4:27:00 AM, mtpagesj at lg.ehu.es writes:
>This looks like a bug in the package Calculus`Limit`
>
>In[1]:= $Version
>Out[1]= "4.0 for Power Macintosh (July 20, 1999)"
>
>In[2]:= << Calculus`Limit`
>
>In[3]:= Limit[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), n -> Infinity]
>Out[3]= 9
>
>The calcultion was done in a G4. The same result was obtained in version
>3
>under windows.
>
It is definitely wrong. It does much better if you simplify the expression
before taking the limit.
Needs["Calculus`Limit`"];
Limit[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), n -> Infinity]
9
(2^(n + 1) + 3^(n + 1))/(2^n + 3^n) // FullSimplify
3 - 1/(1 + (3/2)^n)
Limit[%, n -> Infinity]
3
Plot[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), {n, 0, 20}];
Bob Hanlon