# CCL: Question Szabo/Ostlund Ex.1.14

• From: Jürgen Gräfenstein <jurgen_+_chem.gu.se>
• Subject: CCL: Question Szabo/Ostlund Ex.1.14
• Date: Thu, 3 Nov 2011 20:50:05 +0100

 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