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Unformatted text preview: First Preliminary Exam Math 213 Spring 2008 Name : Solutions This exam has 6 questions on 7 pages, for a total of 50 points. You have 50 minutes to answer all questions. This is closed book, closed notes exam. Use of calculators and other electronic devices is not permitted. Question Points Score 1 12 2 8 3 5 4 10 5 10 6 5 Total: 50 Multiple Choice No partial credit! 1. Multiple Choice. Circle the correct answer for each question. (a) (4 points) Dr. Dorais favorite number is: A. 17 B. 17 C. 17 D. All of the above! Solution: D (but the other three are also correct). (b) (4 points) The limit lim ( x,y ) (0 , 0) sin(17 x 2 17 y 2 ) cos(17 x 2 + 17 y 2 ) A. Equals 1. B. Equals 0. C. Equals 17. D. None of the above. Solution: B: The function is continuous at (0 , 0). (c) (4 points) The function f ( x,y ) = x 2 y 2 + 17 x 17 y + 289: A. Has a local maximum at (0 , 0). B. Has a local minimum at (0 , 0). C. Has a saddle point at (0 , 0). D. None of the above. Solution: D: (0 , 0) is not a critical point of f . Page 2 Short Answer Show your work! 2. Derivatives. (a) (4 points) Compute the gradient of f ( x,y,z ) = y 2 e xz at (1 , 2 , 2)....
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 DORAIS
 Math, Calculus

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