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Limit question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg73072] Limit question
*From*: "dimitris" <dimmechan at yahoo.com>
*Date*: Thu, 1 Feb 2007 03:19:00 -0500 (EST)
Practising with the Limit command I discover the following setting
In[487]:=
(Limit[Log[z], z -> -1, Direction -> #1] & ) /@ {I, -I}
Out[487]=
{(-I)*Pi, I*Pi}
So my simple question is if it is somewhere documented in the
Mathematica Book that you can use other values than just {1,-1} for
the Direction Option. Note that
In[481]:=
Information[Direction]
>From In[481]:=
"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[481]:=
Attributes[Direction] = {Protected}
Note also that even in this link
http://support.wolfram.com/mathematica/kernel/Symbols/
in which for some Built-In functions you can find additional
information (for example
http://support.wolfram.com/mathematica/kernel/Symbols/System/
Oscillatory.html
http://support.wolfram.com/mathematica/kernel/Symbols/System/
Integrate.html )
there is no other information.
Dimitris
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