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