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final_exam_math2500

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

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