I. Consider the vector field = < 0,0 > and let be the part of the cylinder of radius 2 and height 4 which lies in the first octant. That is 4, 0 ≤ ≤ 4, ≥ 0, ≥ 0 (a) Sketch the surface S and the vector field F (b) Do you expect the flux outward across S to be positive, negative or zero? Explain briefly(c) Compute the flux integral ∙ ! (use the normal which points outward from S) (observation: divergence theorem can not be used in part (c) because S is not a closed surface, need to compute this surface integral using the definition)(d) Let D be the solid in the first octant bounded by S together with four other faces (shown below). Use the divergence theorem to compute the flux of the vector field = < 0, 0 > out of the boundary of the region D (e) What is the flux outward through the four faces (use your answers to parts (c) and (d)
