CCL: Question Szabo/Ostlund Ex.1.14

[Jürgen Gräfenstein <jurgen_+_chem.gu.se>]

 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