MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Practice10
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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. Mark for each of the 20 questions the correct letter. For any three points p, q, r in space, ~p q ~p r = ~qp ~rp. The triangle de ned by the three points ( 1, 0, 2), ( 4, 2, 1), (1, 1, 2) has a right angle. The function f (x, y, z) = x2 + y2 + z2/ sin(x2 + y2 + z2) is continuous ev- erywhere in space. ~u ~u = 0 implies ~u = ~0. The level curves f (x, y) = 1 and f (x, y) = 2 of a smooth function f never intersect.
