MATH 21A Midterm: MATH 21A Harvard 21a Fall 16Practice12
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Tth 10 george melvin: 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. Tth 11:30 jake marcinek: you have 180 minutes time to complete your. For any two vectors ~v and ~w one has proj~v(~v ~w) = ~0. Any parameterized surface s is either the graph of a function f (x, y) or a surface of revolution. If the directional derivative d~v(f ) of f into the direction of a unit vector ~v is zero, then ~v is perpendicular to the level curve of f .
