MATH 21A Final: MATH 21A Harvard 21a Fall 17Final
Document Summary
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 length of the gradient f (0, 0) is the maximal directional derivative. |d~vf (0, 0)| among all unit vectors ~v. The relation fxxyyxx = fxxyxyx holds everywhere for f (x, y) = cos(exp(x10)+ sin(x y)). 0 r 4x g(x, y) = r 0. 0 f (s, t) dsdt satis es gxy = f (x, y). 0 f (x, y) dydx = r 16 y/4 f (x, y) dxdy. 0 r 16 y r x h1/ 2,1/ 2i h1/ 2, 1/ 2i f (a, b) = 3 and d.
