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. The bad news now 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? > > Thank you in advance, > > Davide