Re: Limits of Nested Expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg80732] Re: [mg80718] Limits of Nested Expressions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 30 Aug 2007 23:39:03 -0400 (EDT)
- References: <200708300629.CAA08798@smc.twtelecom.net>
On 30 Aug 2007, at 07:29, Yaroslav Bulatov wrote: > Is it possible to compute the following limit in Mathematica 6? > Limit[Nest[Sqrt[5 + #]&, 5, n], n -> Infinity] > > It used to be possible through Calculus`Limit package, which seems to > be gone > > Fortunately this is not longer possible as it was one of the dumbest ideas ever implemented in Mathematica (the Calculus`Limit package did have a few tricks up its sleave but on the whole it was an embarassment for WRI and it is a very good thing that it is gone). It is trivial to find the Limit symbolically (after proving that it exists): First[x /. Solve[Sqrt[5 + x] == x, x]] (1/2)*(1 + Sqrt[21]) Or numerically: FixedPoint[N[Sqrt[5 + #1]] & , 5] 2.79128784747792 Andrzej Kozlowski
- References:
- Limits of Nested Expressions
- From: Yaroslav Bulatov <yaroslavvb@gmail.com>
- Limits of Nested Expressions