MATH 21A Final: MATH 21A Harvard 21a summer 10Finalsol
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Tth 11:30 sebastian vasey: start by printing your name in the above box and check your section in the box to the left, do not detach pages from this exam packet 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. Mark for each of the 20 questions the correct letter. The parametric surface ~r(u, v) = (5u 3v, u v 1, 5u v 7) is a plane. Any function u(x, y) that obeys the di erential equation uxx + ux uy = 1 has no local maxima. The length of the vector projection of ~b onto a vector ~a is smaller or equal than the length of the vector ~b.
