a) State how to use a surface integral to determine the surface area of a surface S. b) Explain briefly how you can use the curl of a vector field to determine if it is conservative. c) Let S be the surface given by x^2+y^2+z^2=1 with z0 and upward orientation. Explain why we cannot use the Divergence Theorem and how we could adapt the problem slightly so that we can. Explain the process and how you would compute the flux, but you do not need to actually set up or evaluate any integrals. d) Let S be the portion of the plane 3x+4y+5z=60 in the first octant. Use a surface integral to determine the surface area of S. e) Let F (x,y,z)= x+z,y+z,z and let S be the surface given by x^2+y^2+z^2=1 with z 0 and upward orientation. Compute _S curl (F) dS using Stokes' theorem