In this exercise, we realize the delta function 5v(a) as a limit of functions on a finite interval [0. i]. Let 0 (a) Prove that the functions

where gn(x) is given by 111.31). and

satisfy (11.29-30). and hence

(b) One can. alternatively, relax the second condition (11.30) to

Show that, under this relaxed definition,
on a finite interval [0,2113].

121 lim x)(r). lim g" (x-y) dx=1.