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Unformatted text preview: z = 2x 2y 2 and z = x 2 + y 2 if the density function is ( x, y, z ) = z . 6. Reverse the order of integration in the integral Z 1 Z y 2 f ( x, y ) dx dy . Math 265 Final Exam Page 4 7. For the vector feld F ( x, y ) = h 3 x 2 y 2 + 2 y, 2 x 3 y + 2 x i , either fnd a potential unction f so that F = f or explain why no such potential unction exists. 8. Find and classiy the critical points o f ( x, y ) = x 2 + y 2 + x 2 y + 4. Math 265 Final Exam Page 5 9. Given the planes x + yz = 2 and 3 x4 y + 5 z = 6: (a) Find the angle between them. (b) Find symmetric equations for their line of intersection. Math 265 Final Exam Page 6 10. Let S be the surface z = 4x 2y 2 with z 0. (a) Compute the surface area of S . (b) Let F = hy, x, xyz 4 i and n the upward normal vector on S . Compute the surface integral RR S F n dS ....
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 Spring '08
 Gregorac
 Math, Calculus

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