This test is closed book and closed notes. A (graphing) calculator is allowed for this test but cannot also be a communication device (i. e. , your iphone is not a calculator). Answer each question completely using exact values unless otherwise indicated. Show your work (legibly); answers without work and/or justi cations will not receive credit. Place your nal answer in the provided box. Each problem is worth 10 points for a total of 80 points. Do not begin this test until instructed to start: when a curve intersects itself the angle of intersection is the angle between the two tangent vectors of the curve at the point of intersection. Find cos where is the angle of intersection of the parametric curve (t2 t, t3 3t2 +2t) at the point (0, 0) (corresponding to the intersection times t = 0 and t = 1). Answer: find the equation in spherical coordinates corresponding to the cylindrical coordinate equation z2 r2 = 9.
