MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Solutions
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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: all functions are assumed to be smooth and nice unless stated otherwise, 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. The parametrization ~r(u, v) = hv2, v2 cos(u), v2 sin(u)i describes a cone. If three vectors ~u, ~v, ~w satisfy ~u ~v = 0 and ~v ~w = ~0, then ~u ~w = 0. Let s be a surface bounding a solid e and ~f is a vector eld in space which is incompressible, div( ~f ) = 0, then rrs.
