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

*To*: mathgroup at smc.vnet.net*Subject*: [mg77979] Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???*From*: Peter Breitfeld <phbrf at t-online.de>*Date*: Thu, 21 Jun 2007 05:29:57 -0400 (EDT)*References*: <f5atqa$b75$1@smc.vnet.net>

jrc schrieb: > 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 > Interestingly Limit seems not to recognize the assumptions of $Assumptions. But you get the desired result, if you input Limit[...,Assumptions->$Assumptions] or an equivalent Assuming[$Assumptions,Limit[...]] Gruss Peter -- ==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-== Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de