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Unformatted text preview: 3. (c) min:√ n , max: √ n . 4. Calculate the double integral. (a) ZZ R 1 + x 2 1 + y 2 dA, R = [0 , 1] × [0 , 1] (b) ZZ R x x 2 + y 2 dA, R = [1 , 2] × [0 , 1] (c) ZZ R cos x + sin y dA, R = [0 ,π ] × [0 ,π/ 2] Answers: (a) π/ 3 (b) 1 2 ln(5 / 2) + 2 tan1 (1 / 2)π/ 4 1 (c) π 5. Find the average value of f ( x,y ) = e y √ x + e y over the rectangle [0 , 4] × [0 , 1]. Answer: ≈ 3 . 327 6. Find the maximum and minimum volumes of a rectangular box whose surface area is 1000 cm 3 and whose total edge length is 200 cm. Answer: 1416 . 5 and 3268 . 35 2...
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 Spring '08
 BOCIU
 Math, Calculus, Rectangle, minimum values

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