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Re: wrong limit ?

• To: mathgroup at smc.vnet.net
• Subject: [mg76797] Re: wrong limit ?
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Sun, 27 May 2007 05:05:34 -0400 (EDT)
• References: <f38tdj$ish$1@smc.vnet.net>

ventu <nuclearVentu at gmail.com> wrote:
> Hi !
> Here's my problem (mathematica 5.0,5.1,5.2):
>
> Limit[Coth[xB], B -> +Infinity]
>
> it doesn't understand.

Having a space between x and B might have helped, but in fact the limit is
then returned unevaluated in version 5.2.

> mmh. ok I try then:
>
> Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0]
>
> 1
>
> WRONG !

Yes, I think you discovered a bug. I wonder if it exists in version 6.

> In fact:
>
> Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0 && Re[x] < 0]
>
> -1
>
> Indeed the correct result should be sign(x).

I presume you're talking about the correct result for
Limit[Coth[x B], B -> Infinity, Assumptions -> Element[x, Reals]]. But no,
Sign[x] would not be correct because Sign[0] is 0, while the limit would be
ComplexInfinity when x is 0.

However, it would be nice if

Limit[Tanh[x B], B -> Infinity, Assumptions -> Element[x, Reals]]

gave Sign[x], rather than, incorrectly, 1.

David W. Cantrell