MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Midterm 2
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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 identity fyxyx = fxyxy holds for all smooth functions f (x, y). Using linearization we can estimate (1. 003)2(1. 0001)4 2 0. 003+4 0. 0001. We have d/dt(x2(t)y(t)) = h2x(t)y(t), x2(t)i hx (t), y (t)i. The function f (x, y) = 3y2 2x3 takes no maximal value on the squircle x4 + y4 = 8. If f (x, t) solves the heat equation then f (x, t) solves the heat equation. If f (x, t) solves the wave equation, then f (x, t) solves the wave equation.
