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2. Here we make a connection between Stokes' Theorem and the Divergence Theorem. 1. Assume G" is a divergence-free vector eld in R3. Consider the upper unit hemisphere surface M = {:132 + y2 + 22 = 1, z 2 0} with outward unit normal. Exhibit 4 different surfaces M1, M2, M3, M4 such that ff -d82/f -dS M,- M for each j = 1, 2,3,4. Make sure to Specify1 your unit nOrmal for each surface Mj and justify why the above surface integrals are equal. 2. Let F = (P, Q, R) be any vector eld in R3. Assume P, Q, R have continuous second par- tial derivatives. Show that the curl of F is divergence-free. That is, show div(curlF) = 0. (This is the same question as problem 12 a) above. You can just cite your solution from 12a) here.)