MATH 21A Final: MATH 21A Harvard 21a Fall 13Final
Document Summary
Tth 11:30 francesco cavazzani: 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 directional derivative d~vf is a vector perpendicular to ~v. Using linearization of f (x, y) = xy we can estimate f (0. 9, 1. 2) 1 0. 1 + Given a curve ~r(t) on a surface g(x, y, z) = 1, then d dt g(~r(t)) = 0. such that f (0, 0) = h2, 1i. ~r(u, v) = hu cos(v), u sin(v), vi is a surface of revolution. If (1, 1) is a critical point for the function f (x, y) then (1, 1) is also a critical point for the function g(x, y) = f (x2, y2).
