Suppose F(x, y, z) = 4i +5yj+3zk. (a) Find the flux of F through the cube...

 

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Suppose F(x, y, z) = 4i +5yj+3zk. (a) Find the flux of F through the cube in the first octant with edge length c, one corner at the origin, and edges along the axes. The cube is oriented outward. Flux through the front face (the plane x = c) is Flux through the back face (the plane x = 0) is Flux through the right face (the plane y = c) is Flux through the left face (the plane y = 0) is Flux through the top face (the plane 2 = c) is Flux through the bottom face (the plane z = 0) is Total flux through the cube = (b) Use the geometric definition of divergence and the total flux to find div(F) at the origin. div (F(0, 0, 0)) = lim c-0 Suppose F(x, y, z) = 4i +5yj+3zk. (a) Find the flux of F through the cube in the first octant with edge length c, one corner at the origin, and edges along the axes. The cube is oriented outward. Flux through the front face (the plane x = c) is Flux through the back face (the plane x = 0) is Flux through the right face (the plane y = c) is Flux through the left face (the plane y = 0) is Flux through the top face (the plane 2 = c) is Flux through the bottom face (the plane z = 0) is Total flux through the cube = (b) Use the geometric definition of divergence and the total flux to find div(F) at the origin. div (F(0, 0, 0)) = lim c-0