H.W.1 calculus 3 Exercise 1 Sketch the curve by eliminating the parameter, and indicate the direction of increasing t. x = 2t + 3, y = 4t − 5 x = sin t y = 2 cos t Exercise 2 Find the slope of the tangent line on the following curve that correspond to t = 1. x = t2 + 1 y = t3 Exercise 3 Find the length of the curve. x = 2t, y = t3/2 , 0 ≤ t ≤ 1 Exercise 4 Find the center and radius of the sphere that has (1, −1, 1) and (0, 2, 3) as endpoints of a diameter Exercise 5 Describe the surface whose equation is given by Exercise 6 Find u.v and Exercise 7 Let u×v u = (1, 2, 3) where and u = (1, 3, 5), v = (−1, 0, −2). v on u. x2 + z 2 + z 2 + 2x − 2y + 4z + 6 = 0 v = (2, −1, 3). Find orthogonal projection of orthogonal pro jection of Exercise 8 Let u = 2i − 3j + k, v = 4i + j − 3k, Find the volume of the parallelepiped generated by 1 w = j + 5k. u, v, w u on v and