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PS8_answers - Math 237 A2 A3 A4 A9 i ii iii iv v A10 A11...

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Math 237 Problem Set 8 Answers A2. π 2 A3. 1 2 (1 - 1 e ). A4. i) 1 2 (cos 1 - 1) ii) 1 - sin 1. A9. i) R 3 - 1 R 3 - 3 R 0 - 2 f ( x, y, z ) dz dy dx . ii) R b - b R a q 1 - y 2 b 2 - a q 1 - y 2 b 2 R 3 1 f ( x, y, z ) dz dx dy. iii) R b 0 R a (1 - y b ) 0 R c ( 1 - x a - y b ) - c ( 1 - x a - y b ) f ( x, y, z ) dz dx dy. iv) R 5 0 R tan - 1 (1 / 2) 0 R 2 π 0 ρ 2 sin φf ( ρ sin φ cos θ, ρ sin φ sin θ, r cos φ ) dθ dφ dρ v) R 2 π 0 R 2 0 R 1 - r 2 - 3 - r 2 rf ( r cos θ, y, r sin θ ) dy dr dθ. A10. R 1 0 R 1 - x 0 R 1 - x - y
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