Question

1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r + 4y to evaluate the integral y= (3x2 +14ry +82) dax dy a field F P(a, y)i + Q(x, y)j in the ry-plane such that at each point (r, y) (0,0), F is a unit vector pointing to the origin. 3. Find #2 da +2y dy+2xz dz does not depend 4. Show that the value of on the path taken from A to B JA 5. What can be said about the curl of a conservative two-dimensional vector field? Please explain as best you can i+ (e + tan over the cardioid a + a cos 0, 6. Find the outward flux of the field F 3ry = 1 + 1/2 a > 0 7. Chapter 12 Review (a) p871 no. 23 (b) p853 no. 39 (c) 845 no. 21 8. Chapter 13 Review (a) p900 no. 23

please help ! Q1-Q6

Answer 1

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The me integral of funchon of he path inde pndin a vechoy form F PT Qft f and only i Yot F - P 2.y fax2) - Yot F fay) 2 2y (2) o - (u)+() (22) parh ndapondent Yot F JA

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