Re: wrong limit ?

• To: mathgroup at smc.vnet.net
• Subject: [mg76802] Re: wrong limit ?
• From: dimitris <dimmechan at yahoo.com>
• Date: Sun, 27 May 2007 05:08:09 -0400 (EDT)
• References: <f38tdj\$ish\$1@smc.vnet.net>

```The good news first...

In[5]:=
f[x_, a_] := Coth[a*x]

In[8]:=
(Plot[f[x, #1], {x, 0, 10}, Axes -> False, Frame -> True] & ) /@ {-2,
2}

In[16]:=
(Limit[f[x, a], x -> Infinity, Assumptions -> #1[a, 0]] & ) /@
{Greater, Less}
Out[16]=
{1, -1}

which is correct.

In[18]:=
Limit[f[x, a], x -> Infinity, Assumptions -> Element[a,Reals]]
Out[18]=
1

which as you noticed it is incorrect. You didn't do a mistake.
It is just Mathematica shows a buggy behavior here.

Dimitris

/  ventu       :
> Hi !
> Here's my problem (mathematica 5.0,5.1,5.2):
>
> Limit[Coth[xB], B -> +Infinity]
>
> it doesn't understand.
> mmh. ok I try then:
>
> Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0]
>
> 1
>
> WRONG ! In fact:
>
> Limit[Coth[x B], B -> +Infinity, Assumptions ->  Im[x] == 0 && Re[x] <
> 0]
>
> -1
>
> Indeed the correct result should be sign(x). And I couldn't find a way
> to get it right.
> Do I mistake something?
>