Answer to Question #257390 in Calculus for Smit

Question

(i) Calculate divergence A = x²zî - 2y³z²ĵ+ xy²zk at the point (1,-1,1).

Answer 1

$\dfrac{\partial A_x}{\partial x}=2xz, \dfrac{\partial A_y}{\partial y}=-6y^2z^2,\dfrac{\partial A_z}{\partial z}=xy^2$

$divA=2xz-6y^2z^2+xy^2$

$divA|_{(1,-1,1)}=2(1)(1)-6(-1)^2(1)^2+1(-1)^2$

$=-3$