Math_317_December_2008

Math_317_December_2008 - Math 317, Fall 2008, Section 101...

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Math 317, Fall 2008, Section 101 Page 1 of 2 Final Exam December 8, 2008 15:30 – 18:00 No books. No notes. No calculators. No electronic devices of any kind. The duration of this exam is 150 minutes. There are 10 problems, each worth an equal number of points. Problem 1. (6 points) This problem is about the logarithmic spiral in the plane ~ r ( t ) = e t h cos t, sin t i , t R . (a) Find the arc length of the piece of this spiral which is contained in the unit circle. (b) Reparametrize the logarithmic spiral with respect to arc length, measured from t = -∞ . Problem 2. (6 points) Find the point in the first quadrant where the graph of the function y = 1 3 x 3 has maximal curvature. Problem 3. (6 points) Under the influence of a force field ~ F , a particle of mass 2 kg is moving with constant speed 3 m/s along the path given as the intersection of the plane z = x and the parabolic cylinder z = y 2 , in the direction of increasing y . Find ~ F at the point (1 , 1 , 1). (Length is measured in m along the three coordinate axes.)
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This note was uploaded on 04/28/2010 for the course MATH 12 taught by Professor Fas during the Spring '10 term at Aarhus Universitet.

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Math_317_December_2008 - Math 317, Fall 2008, Section 101...

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