Re: Bug with Limit?

*To*: mathgroup at smc.vnet.net*Subject*: [mg73909] Re: Bug with Limit?*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sat, 3 Mar 2007 00:56:07 -0500 (EST)*References*: <es91g4$34b$1@smc.vnet.net>

This issue has discoused several times on this forum. There is even a relevant thread two or three days ago. In[2]:= Information@Limit >From In[2]:= "Limit[expr, x->x0] finds the limiting value of expr when x approaches x0." >From In[2]:= Attributes[Limit] = {Listable, Protected} Options[Limit] = {Analytic -> False, Assumptions :> $Assumptions, Direction -> Automatic} In[3]:= Information@Direction >From In[3]:= "Direction is an option for Limit. Limit[expr, x -> x0, Direction -> 1] computes the limit as x approaches x0 from smaller \ values. Limit[expr, x -> x0, Direction -> -1] computes the limit as x approaches x0 from larger values. Direction -> Automatic \ uses Direction -> -1 except for limits at Infinity, where it is equivalent to Direction -> 1." >From In[3]:= Attributes[Direction] = {Protected} In[5]:= Limit[Abs[x]/x, x -> 0] == Limit[Abs[x]/x, x -> 0, Direction -> -1] == = Limit[Abs[x]/x, x -> 0, Direction -> Automatic] Out[5]= True In[7]:= (Limit[1/(x - 3), x -> 3, Direction -> #1] & ) /@ {-1, 1} Out[7]= {Infinity, -Infinity} Regards Dimitris =CF/=C7 Sergio Miguel Terrazas Porras =DD=E3=F1=E1=F8=E5: > Hi guys, > > I was teaching a class and was discussing discontinuous functions. > We came across f(x) = Abs(x)/x, and g(x) = 1/(x-3). > The first does not have a limit as x -> 0 and the second does not have a > limit as x -> 3. > The unilateral limits of both are different. > When I specified the direction, Mathematica 5.1 gave the correct answer. > However, when no direction was specified, Mathematica 5.1 gave (seemingly) > by default the value of de right handside limit. > > This is plain wrong, and could lead to problems, specially for a student. > Any comments? > > Thank you. > Sergio Terrazas