Re: Limit and Abs
- To: mathgroup at smc.vnet.net
- Subject: [mg31235] Re: Limit and Abs
- From: "Alan Mason" <swt at austin.rr.com>
- Date: Sat, 20 Oct 2001 04:27:09 -0400 (EDT)
- References: <9qjjho$j80$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hello, I think you've got things reversed (and there's a typo-- n->Infinity should be a->Infinity). The first limit (without Abs)correctly comes back unevaluated because the limit doesn't exist. Cot[a]/(Cot[a]+2) = 1 - 2/(Cot[a] + 2) and Cot[a] takes all values from minus to plus Infinity as a gets large. Amusingly, Version 4.1 gives 1 as the limit for the second expression (with Abs). And this is *incorrect* for a similar reason-- Abs[Cot[a]] takes on all values in [0, Infinity) as a gets large. Alan "Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de> wrote in message news:9qjjho$j80$1 at smc.vnet.net... > Hallo, > > if I evaluate > Limit[Cot[a]/(Cot[a]+2),a->Infinity] > i get the correct answer. > > But I want to evaluate > > Limit[Abs[Cot[a]]/(Abs[Cot[a]]+2),n->Infinity] > > and that's being returned unevaluated. Help states, that Limit will return > expressions unevaluated, if there are functions with unknown behaviour (Abs > unknown ??) so I'm not too surprised or disappointed. > But anyway, how can I workaround or bypass this problem, maybe an option or > another function in the extra packages ? > > Thanks > > Oliver Friedrich > >