MATH 21A Midterm: MATH 21A Harvard 21a Fall 13Practice2
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Tth 11:30 francesco cavazzani: 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. 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). Every point on the parametric curve ~r(t) = ht, t2, ti lies on the surface xz + y = 0. The two surfaces f (x, y, z) = 3 and f (x, y, z) = 5 of the function f (x, y, z) =
