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
>
>

```

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