Use the divergence theorem to compute the net outward flux of the following field across the given surface s.

f = < 8y^2 - 3x, -9x+4y, -2y^3 +z >

s is the sphere {(x, y,z): x^2 + y^2 + z^2 = 9}

find net outward flux across the surface.

Flux across S = 72π

Step-by-step explanation:

First we need to calculate the divergence of the vector field:

Div F =

Where

Fx = 8y^2 - 3x

Fy = -9x+4y

Fz = -2y^3 +z

Then

Div F = -3 +4 + 1  = 2

And how the vector field’s divergence is a constant, we can calculate the flux across of the surface how:

Flux across S = Div F * Volume of Sphere

Fluz acroos S = 2(4/3)π

                 r : Sphere’s radio

Flux across S = (2)(4/3)π

                       = 72π

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.