MATH 227 Study Guide - Midterm Guide: Unit Circle
Document Summary
Be sure that this examination has 12 pages including this cover. A skier descends the hill z = p4 x2 y2 along a trail with parameterization. 0 y = 1 cos(2 ), Find, at p , z = 2 cos , 2 (i) the rate of change of the skier"s speed and (ii) the skier"s velocity (a vector). Let (x, y) = xy and let f = . (a) find an equation for the eld line of f which passes through the point (3, 2). Sketch it and verify that it also passes through (3, 2). (b) find r (3,2) (3, 2) F dr, where the line integral is along the eld line of (a). Find the surface area of the torus obtained by rotating the circle (x 3)2 + z2 = 4, y = 0 about the z axis. Let s be the portion of the sphere x2 + y2 + z2 = 36 with y + z 6.
