final_exam_math2500 - MATH 2550 Final Exam December 8, 2006...

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MATH 2550 Final Exam December 8, 2006 NAME (please print legibly): Please complete all 10 questions in the space provided. You may use the backs of the pages for extra space, or ask me for more paper if needed. Work carefully, and try to complete the problems you find easier before going back to the harder ones. Good luck! QUESTION VALUE SCORE 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 TOTAL 120 1
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1. (10 points) Two curves f ( t ) and g ( t ) are given by f ( t ) = 2 2 (cos t, sin t, t ) and g ( t ) = ± 1 2 t 2 , 2 2 3 t 3 / 2 , t ! . (Sorry about the weird-looking coefficients!) where t ranges from 0 to 10 . Which curve is longer? ANSWER: 2
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A function f ( x, y ) has the gradient vector f = (3 , 4) at the point (0 , 0) . What is the directional derivative of f in the direction (1 , 4) ? ANSWER: Find a direction ~v in which the directional derivative of f is equal to zero. ANSWER:
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This note was uploaded on 03/12/2012 for the course MATH 2500 taught by Professor Staff during the Spring '08 term at University of Georgia Athens.

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final_exam_math2500 - MATH 2550 Final Exam December 8, 2006...

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