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Re: Very simple limit, why doesn't it evaluate?
"Andrzej Kozlowski" <andrzej at bekkoame.ne.jp> wrote in message news:9v77po$s5v$1 at smc.vnet.net... > Computing limits is done by means of a number of ad hoc tricks rather > than a universal algorithm, so there will always be cases that > Mathematica can't manage but can be done "by hand". In general when > Mathematica can't find a limit it is a good idea to load in the > Calculus`Limit` package and try again. In this case this case we get: > > << Calculus`Limit` > > In:= > Limit[4^(3 + n)/(-5 + 3^(4 + n)), n -> Infinity] > > Out= > Infinity > > This is with Mathematica 4.1 so I am not sure what happens with 3.0 but > I suspect the same thing. > Unfortunately calculating limits is not easy and currently I would not bother using Mathematica for this purpose, since the results would have to be verified by hand (brain?) anyway. It might fail to solve a trivial example, or even give a wrong answer. For example, the Calculus `Limit` package when asked for Limit[(3^n)/(3^(n + 1) +1), n -> Infinity] says 1, while the correct answer is 1/3; Limit[(3^n)/(3^(n + 2) +1), n -> Infinity] is given as 1/3 (should be 1/9). The built-in function does give the correct answers to these, but then it fails on other equally simple cases. Mathematica Limit certainly is no Augustin Cauchy and will never be, but it seems it easily could/should be a little smarter than it is now. It needs some work. MG