m251fin_sample

# m251fin_sample - MATH 251.509 NAME Final Examination...

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Unformatted text preview: MATH 251.509 NAME Final Examination SIGNATURE May 10, 2006 This exam consists of 15 problems, numbered 115 . For partial credit you must present your work clearly and understandably and justify your answers. The use of calculators is not permitted on this exam. The point value for each question is shown next to each question. CHECK THIS EXAMINATION BOOKLET BEFORE YOU START. THERE SHOULD BE 15 PROBLEMS ON 9 PAGES (INCLUDING THIS ONE). Do not mark in the box below. Points Possible Credit 110 70 11 16 12 18 13 18 14 18 15 10 Total 150 NAME MATH 251 Final Examination Page 2 Multiple Choice: [7 points each] In each of Problems 110, circle the best answer . 1. The function f ( x, y ) = x 2 y 2- 4 x- y has a critical point at ( x, y ) = ( 1 2 , 2 ) . According to the Second Derivative Test, this point is (A) a local minimum. (B) a local maximum. (C) a saddle point. (D) an inflection point. (E) none of the above. The Second Derivative Test fails . 2. Find the area of the parallelogram with vertices (0 , , 0), (2 , 1 , 1), (3 , 4 , 1), and (1 , 3 , 0). (A) 35 (B) 59 (C) 35 (D) 59 (E) 5 3. Calculate ZZ R 1 x 2 + y 2 dA , where R is the ring-shaped region in the xy-plane between the circles x 2 + y 2 = 9 and x 2 + y 2 = 16....
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## m251fin_sample - MATH 251.509 NAME Final Examination...

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