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

• To: mathgroup at smc.vnet.net
• Subject: [mg77959] Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???
• From: jrc <jrchaff at mcn.net>
• Date: Wed, 20 Jun 2007 05:41:19 -0400 (EDT)

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

• Follow-Ups:
  • Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone
    • From: Carl Woll <carlw@wolfram.com>
  • Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>