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Unformatted text preview: 1 MATH 203 Final Exam, December 17, 2009 Instructions: Complete every question in Part I (Questions 1-7.) Complete three of the five questions in Part II (Questions 8-12). Each question is worth 10 points. No calculators or other electronic devices may be used during the examination. Answers may be left in terms of 7 , sin(3) , , etc. Give reasons for all answers. This exam will last 2 hours and 15 minutes. Good luck! PART I: Answer all parts of Questions 1-7. Each question is worth 10 points 1. Let P be the plane that contains the points (1 ,- 2 , 2), (- 2 ,- 1 , 4) and (- 1 ,- 3 , 2). (a) Give an equation for the plane P . (b) Parameterize the line of intersection between P and the plane z = 1. 2. Given that f ( x,y,z ) = x 3 y 2 + ye 2 z . (a) Evaluate f . (b) Find the rate of change of f at (2 ,- 1 , 0) in the direction of h- 2 ,- 2 ,- 1 i . (c) Find an equation of the tangent plane to the surface x 3 y 2 + ye 2 z = 7 at the point (2 ,- 1 , 0)....
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