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.