7. Use the divergence theorem to calculate the ux of F = (a: y) i + (y z) j + (z :17) k out of
7. Use the divergence theorem to calculate the ux of F = (a: y) i + (y z) j + (z :17) k out of the unit sphere 51:2 + y2 + 22 = 1. 4. Let F = w2i+ (2wy+w)j+zk. Let C be the circle :I;2+y2 = 1 and S the disk w2+y2 S 1 within the plane 2 = 0. (a) Determine the ux of F out of S. (b) Determine the circulation of F around 0'. (c) Find the ux of V X F. Verify Stokes' theorem directly in this case
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