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

*To*: mathgroup at smc.vnet.net*Subject*: [mg78003] Re: [mg77959] Same Limit: OK in 5.2, fails in 6.0; Packages gone*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 21 Jun 2007 05:42:23 -0400 (EDT)*References*: <200706200941.FAA10343@smc.vnet.net>

jrc 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. This is a glitch in Limit handling of $Assumptions. It was written to work with an Assumptions option and sometimes messes up the more global $Assumptions. Offhand I do not know why it did not also mess up in version 5.2. Workarounds include (1) Use explicit And (instead of List) for $Assumptions. $Assumptions = Apply[And,{a>0,k1>0,k2>0,Element[x,Reals]}] In[10]:= Limit[i1b, a->Infinity] Out[10]= 0 (2) Use Assumptions option in Limit. In[12]:= $Assumptions = . In[13]:= ClearSystemCache[] In[14]:= Limit[i1b, a->Infinity, Assumptions->{a>0,k1>0,k2>0,Element[x,Reals]}] Out[14]= 0 We'll get the underlying problem fixed. > 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. That claim was a stretch. By any reasonable metric that package made Limit substantially more error-prone. Which is why the package is gone. > How many packages no longer exist in 6.0 ???? Is there a list ???? > > Can anyone give me a reason for this obvious failure? > > jrc Daniel Lichtblau Wolfram Research

**References**:**Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???***From:*jrc <jrchaff@mcn.net>