       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:=
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=
Integrate[E^(I*k*x), {x, -Infinity, Infinity}]

In:=
(1/Sqrt[2*Pi])*FourierTransform[1, x, k]
Out=
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.