From owner-chemistry-: at :-ccl.net Thu Nov 3 16:02:01 2011 From: "=?iso-8859-1?Q?J=FCrgen_Gr=E4fenstein?= jurgen[*]chem.gu.se" To: CCL Subject: CCL: Question Szabo/Ostlund Ex.1.14 Message-Id: <-45818-111103155015-20121-XJqhZl2QNAfWPRksmtnE9g-.-server.ccl.net> X-Original-From: =?iso-8859-1?Q?J=FCrgen_Gr=E4fenstein?= Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="iso-8859-1" Date: Thu, 3 Nov 2011 20:50:05 +0100 MIME-Version: 1.0 Sent to CCL by: =?iso-8859-1?Q?J=FCrgen_Gr=E4fenstein?= [jurgen%a%chem.gu.se] Dear Martin, Start from the (first) mean value theorem of integral calculus (http://en.wikipedia.org/wiki/Mean_value_theorem#Mean_value_theorems_for_integration). You need to assume that function a is continuous (otherwise the theorem does not hold). Best regards, Jürgen On 3 Nov, 2011, at 16:56 10, Martin Hediger ma.hed-x-bluewin.ch wrote: > > Sent to CCL by: "Martin Hediger" [ma.hed^^bluewin.ch] > Dear List > I also posted this question to the google.gamess user group, but was encouraged to do so here. I'm new to the CCL and looking forward to interesting discussions. > > I was trying to solve ex. 1.14 from Szabo/Ostlund. If > > d(x) = \lim_{eps->\infinity} d_eps(x), > > where > > d_eps(x) = 1/(2eps) when -eps <= x <= eps and d_eps(x)=0 else, > > we are supposed to show that > the value of a function a(0) = \int dx a(x) d(x) > > My Ansatz was to insert the definition into the integral, but then I'm > not exactly seeing how to treat the limit function. > How does one show this? > > Thank you for any suggestions. > Martin