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Re: Limit of nested function

• To: mathgroup at smc.vnet.net
• Subject: [mg122170] Re: Limit of nested function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 18 Oct 2011 07:41:03 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110162045.QAA19694@smc.vnet.net>

You can do it this way at all. In fact, using a little mathematics you 
can show that your iteration has two fixed points x=0 and x=1. x=1 
is an attractor and if you start iteration from any positive number the 
limit will be 1. E.g.

In[50]:= FixedPoint[Sqrt[# Sqrt[#]] &, 1.2]

Out[50]= 1.

In[51]:= FixedPoint[Sqrt[# Sqrt[#]] &, 100.]

Out[51]= 1.

In[52]:= FixedPoint[Sqrt[# Sqrt[#]] &, 0.01]

Out[52]= 1.

You are expecting far too much from a computer program ...

Andrzej Kozlowski



On 16 Oct 2011, at 22:45, Miguel wrote:

> How can I to calculate the limit of a nested function . Mathematica 6
> yields an error message "... Non negative machine size integer ...".
>
> For example, let
>
>
> f[x,n]=Nest[Sqrt[# Sqrt[#]]&,x,n]
>
> For x=3,      Limit[f[3,n], n->inf]
>
> Thanks
>
>

• References:
  • Limit of nested function
    • From: Miguel <mibelair@hotmail.com>