MATH 222 Final: MATH 222 KSU Final Exam s04
15 Feb 2019
School
Department
Course
Professor
Document Summary
To receive credit you must show your work. (20) 1. An object is moving in 3-space along the parametric curve. ~r(t) = ht + 1, sin t, cos ti. An object is moving in the plane along the curve y = sin x, in the direction of increasing x. Its speed is constant at 2 ft/sec. (a) find a ~t and a ~n when the object is at (x, sin x). (b) find the velocity vector and the acceleration vector when the object is at. Find an equation for the tangent plane to the given surface s at the given point p . (a) s : ellipsoid 2x2 + y2 + z2 = 4. P : (1, 1, 1) (b) s : the torus given parametrically by. ~r(u, v) = h(2 + cos v) cos u, (2 + cos v) sin u, sin vi. P : the point given by u = v = /2 (15) 5.
