MATH 21A Midterm: MATH 21A Harvard 21a summer 10Practice3
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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. Problem 1) true/false questions (20 points), no justi cations needed. The point ( 5, 3) is a critical point of f (x, y) = 3x2 + 5y2. If a function f (x, y, z) has gradient satisfying | f| = 1 everywhere, then the level surface f (x, y, z) = 1 is a sphere. The chain rule assures that the vector f (~r(t)) and the velocity vector ~r (t) for any curve ~r(t) on the level surface are perpendicular. xy satis es the formula d ~dd = d ~d for. The function d(x, y) = fxxfyy f 2 any unit vector ~d.
