[Date Index]
[Thread Index]
[Author Index]
Re: Limit and Abs
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31230] Re: Limit and Abs
*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>
*Date*: Sat, 20 Oct 2001 04:27:03 -0400 (EDT)
*References*: <200110170935.FAA19657@smc.vnet.net> <9qokm5$mt3$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Tomas Garza <tgarza01 at prodigy.net.mx> wrote:
> And what, may I ask, is the "correct answer"? Your function is periodic
> with period Pi. The only answer is
>
> In[1]:=
> Limit[Cot[a]/(2 + Cot[a]), a -> Infinity]
>
> Out[1]=
> Limit[Cot[a]/(2 + Cot[a]), a -> Infinity]
>
> And, unless there is a misprint in your second expression below, the
> limit with *n* -> Infinity has to remain unevaluated, because a is not
> defined. But, then, if there is a misprint and you meant a -> Infinity
> instead of n->Infinity,
As we now know, he didn't mean either! But taking a -> Infinity does
raise an interesting point.
> the function is again periodic with period Pi
> (look at the graphs). The limit doesn't exist, and Mathematica has no
> alternative but to leave the expression unevaluated.
False! As others have pointed out, Mathematica does have other
alternatives, and the one it chooses, returning a limit of 1, is
incorrect. In my opinion, it should have returned Interval[{0,1}]
as the answer instead. Mathematica has a more generalized notion of
limit than is often used. For example, although most of us would
normally say simply that Limit[Sin[a], a -> Infinity] does not exist,
Mathematica gives Interval[{-1,1}]. This is correct in a sense. I have
no objection to it; indeed, it provides more useful information than
merely saying "does not exist".
David Cantrell
> From: "Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de>
To: mathgroup at smc.vnet.net
> Subject: [mg31230] Limit and Abs
>
> > 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.
--
-------------------- http://NewsReader.Com/ --------------------
Usenet Newsgroup Service
**References**:
**Limit and Abs**
*From:* "Oliver Friedrich" <oliver.friedrich@tz-mikroelektronik.de>
Prev by Date:
**RE: Switching x and y axes in 2D plots**
Next by Date:
**How to set font size?**
Previous by thread:
**Re: Limit and Abs**
Next by thread:
**Re: Re: Limit and Abs**
| |