Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???

*To*: mathgroup at smc.vnet.net*Subject*: [mg78009] Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???*From*: "Rolf.Mertig at gmail.com" <Rolf.Mertig at gmail.com>*Date*: Thu, 21 Jun 2007 05:45:28 -0400 (EDT)*References*: <f5atqa$b75$1@smc.vnet.net>

Hi, yes, there is a problem with Limit recognizing $Assumptions. Find below a workaround. Regards, Rolf Mertig http://www.gluonvision.com Mathematica 6.0 for Linux x86 (32-bit) Copyright 1988-2007 Wolfram Research, Inc. In[1]:= !!limit $Assumptions={a > 0, k1 > 0, k2 >0,Element[x,Reals]}; SetOptions[Limit, Assumptions -> $Assumptions]; i1b=1/a Integrate[Exp[-I k2 x] Exp[I k1 x],{x,-a/2,a/2}] Limit[i1b, a -> Infinity] In[1]:= <<limit Out[1]= 0 On Jun 20, 11:59 am, jrc <jrch... at mcn.net> wrote: > Why? > > I have, > > $Assumptions = {a > 0, k1 > 0, k2 >0, x e(in) Reals} > (repeats ok) > > i1b = (1/a)* Integral from -a/2 to +a/2 of integrand: > > exp(- i k2 x) exp(i k1 x) dx > > with the expected result, > > i1b = fraction with numerator = 2 Sin[(1/2)a(k1-k2)] > and denominator = a(k1-k2) > > Now I want the limit of this result, as the parameter a goes to infinity: > > Limit[i1b, a -> Infinity] > > Mathematica 5.2 gives correct result, zero; > (note this is just lim(sin(x)/x, x -> inf), which is obviously zero) > > Mathematica 6.0 is unable to evaluate the limit. > > Ruskeepaa's "Navigator", 2nd ed, (written for v5.2) claims there > is a package, "Calculus`Limit`" that makes 'Limit' work better > (p. 395 and p. 430). However, no such package seems to exist in > v6.0. > > How many packages no longer exist in 6.0 ???? Is there a list ???? > > Can anyone give me a reason for this obvious failure? > > jrc