MATH 21B Midterm: MATH 21B Harvard 21b Fall 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 function f (x, y) = x3y/(x6 + y5) can be lled in at the origin with a value f (0, 0) = a so that f is continuous everywhere. 0 ( f (~r(t)) ~r (t)) dt = f (~r(1)) f (~r(0)). If u(x, t) solves the partial di erential equation ut = ux, then so does the function ux. There is a surface s containing the curve ~r(t) = ht, t2, t3i for which the tangent plane to s at (0, 0, 0) is x + 2y + 3z = 0.
