MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Practice7
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Tth 11:30 george melvin: print your name in the above box and check your section, do not detach pages or unstaple the packet, please write neatly. Answers which are illeg- ible for the grader cannot be given credit: show your work. Except for problems 1-3, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 180 minutes time to complete your work. ~g d~s for any closed surface s. The parametrization ~r(u, v) = hcos(u), sin(u), vi describes a cone. The vectors ~v = h2, 1, 5i and ~w = h2, 1, 1i are perpendicular. Let e be a solid region with boundary surface s. if rrs div( ~f )(x, y, z) = 0 everywhere inside e. ~f d~s = 0 for any closed surface. If div( ~f )(x, y, z) = 0 for all (x, y, z) then rrs.
