MATH 21A Midterm: MATH 21a Harvard 21a Fall 12Practice1
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Mark for each of the 20 questions the correct letter. Tth 11:30 andrew cotton-clay: 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, and 5, we need to see details of your compu- tation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. If two planes ax + by + cz = d and ax + by + cz = d are parallel then a = a, b = b, and c = c. The point (x, y, z) = (1, 1, 2) has the spherical coordinates ( , , ) = (2, /4, /4).
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