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MathGroup Archive 2007

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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


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