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MathGroup Archive 2001

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Re: Limit and Abs

  • To: mathgroup at
  • Subject: [mg31210] Re: Limit and Abs
  • From: Jens-Peer Kuska <kuska at>
  • Date: Fri, 19 Oct 2001 03:12:00 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <9qjjho$j80$>
  • Sender: owner-wri-mathgroup at


what Mathematica version ??

Mathematica 4.1 say

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

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

Your first example gives

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}]


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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