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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20E Midterm Exam 1 October 24, 2008 Turn off and put away your cell phone. You may use one page of notes, but no calculators, books or other assistance. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 14 2 12 3 12 4 10 48 1. Consider the curve c ( t ) = (sin 2 t, cos 2 t, 2 t ) in R 3 for 0 t . a. (3 points) Draw a careful sketch the graph of c ( t ), clearly labeling the starting point, ending point, and direction of motion. Solution: The graph is one loop of a helix. The starting point is (0 , 1 , 0) and the ending point is (0 , 1 , 2 ). b. (5 points) Find the velocity and acceleration vectors at t = 3 , and show that the velocity v ( t ) and the acceleration a ( t ) are perpendicular for all...
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