       Re: Limit and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg31210] Re: Limit and Abs
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 19 Oct 2001 03:12:00 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <9qjjho\$j80\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

what Mathematica version ??

Mathematica 4.1 say

In[]:=Limit[Abs[Cot[a]]/(Abs[Cot[a]] + 2), a -> Infinity]
Out[]=1

while a picture quickly show that Abs[Cot[a]]/(Abs[Cot[a]] + 2)
oscillate between 0 and 1 and the limit does not exist

In[]:=Limit[Cot[a]/(Cot[a] + 2), a -> Infinity]
Out[]=Limit[Cot[a]/(2 + Cot[a]), a -> Infinity]

and finaly I would like to know what is the "correct
answer" because I would assume that the limit
is undefined/does not exist as to see from

Plot[Cot[a]/(2 + Cot[a]), {a, 0, 100}]

Regards
Jens

Oliver Friedrich wrote:
>
> 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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