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Re: Bug with Limit?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg73979] Re: Bug with Limit?
*From*: "dimitris" <dimmechan at yahoo.com>
*Date*: Sat, 3 Mar 2007 23:56:33 -0500 (EST)
*References*: <es91g4$34b$1@smc.vnet.net>
BTW,
Someone must read carefully the documentation of one command,
search in the MathGroup archives or/and pick up some of the hundreds
books about mathematica before coming to the conclusion that he "just
encountered a bug"!
For example
In[117]:=
Integrate[Exp[I*k*x], {x, -Infinity, Infinity}]
\!\(Integrate::"idiv" \(\(:\)\(\ \)\) "Integral
of \!\(\[ExponentialE]\^\(\[ImaginaryI] \\\\ k \\\\ x\)\)
does not \
converge on {\!\(\(-=E2=88=9E\), =E2=88=9E\)}."\)
Out[117]=
Integrate[E^(I*k*x), {x, -Infinity, Infinity}]
In[116]:=
(1/Sqrt[2*Pi])*FourierTransform[1, x, k]
Out[116]=
DiracDelta[k]
Do you see something buggy here?
Think twice before you answer; the result is not!
Currently only the integral transforms will return distributions in
their output for inputs that do not contain distributions.
Functions like D and Integrate know how to deal with certain
distributions, but their output will only contain
them when their input does.
So, everything is ok!
Regards
Dimitris
=CE=9F/=CE=97 Sergio Miguel Terrazas Porras =CE=AD=CE=B3=CF=81=CE=B1=CF=88=
=CE=B5:
> 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
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