Re: Limit[f[x], x->a] vs. f[a]. When are they equal?
- To: mathgroup at smc.vnet.net
- Subject: [mg118557] Re: Limit[f[x], x->a] vs. f[a]. When are they equal?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 3 May 2011 05:43:59 -0400 (EDT)
On 2 May 2011, at 17:24, Richard Fateman wrote: > On 5/2/2011 6:49 AM, Andrzej Kozlowski wrote: > > ... >> I guess I would prefer the answer ComplexInfinity but this is not necessary since, for example, Sin[x]/x also returns Indeterminate rather than 1 at 0. > > I think you mean ... at ComplexInfinity. > >> This is the kind od thing any user can decide for himself by explicitly defining g[ComplexInfinity]=ComplexInfinity. >> >> There is absolutely nothing here that in any way disagrees with any mathematics I know of. > let r[x_]:=Sin[x]/x. > > Limit[r[x],x->Infinity] is 0 That's the right answer of course! > Limit[r[x],x->ComplexInfinity] is unevaluated. That's also the right answer. The limit does not exist. You can again check that with Mathematica: Limit[Sin[x]/x, x -> ComplexInfinity, Direction -> I] Infinity But Limit[Sin[x]/x, x -> ComplexInfinity, Direction -> 1] Out[108]= 0 One directional limit is finite while another is infinite. The fore obviously there can be no undirected limit. In fact, if you knew a little more mathematics, that would be obvious to you. Esentially all these "problems" derive from a single source - your poor mathematical background. You sure would have problems passing my analytic functions course. Andrzej Kozlowski