(a). Show that (r)/r = (r) when it appears as part of the integrand of...

(a). Show that δ(r)/r = −δ^’ (r) when it appears as part of the integrand of a three-dimensional integral in spherical coordinates. Convince yourself that the test function ∫ (r) does not provide any information. Then try ∫ (r)/r.

(b). Show that ∇ · [δ(r − a)ˆr] = (a²/r²)δ’ (r − a) when it appears as part of the integrand of a three dimensional integral in spherical coordinates.