MATH 21A Final: MATH 21A Harvard 21a Fall 14Final
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Tth 11:30 jameel al-aidroos: 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. Every function f (x, y) of two variables has either a global minimum or a global maximum. The linearization of the function f (x, y) = ex+3y at (0, 0) is l(x, y) = 1 + x + 3y. The function f (x, y, z) = x2 cos(z) + x3y2z + (y 2)3y5 satis es the partial di erential equation fxyxzxy = 12. If xez = y2z, then z/ x = ez/(y2 xez). The function cos(x2) cos(y2) has a local maximum at (0, 0). The value of the double integral r /4 (r 2.
