Set 11 Solutions (1).pdf - ESE 318-02 Fall 2018 Homework...

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ESE 318-02, Fall 2018 Homework Set #11 (10 problems) Due Tuesday, Nov. 20 1 . Zill 9.9.3. 2 . Zill 9.9.10. 3 . Zill 9.9.12. 4 . Zill 9.9.16. (a) First use Theorem 9.9.4 of Zill to show it’s not conservative. (b) Try the “easy way” by finding a “potential, ”, then show that its gradient does not equal F . 5 . Zill 9.9.19. 6 . Zill 9.9.22. 7 . Zill 9.9.24. 8 . Zill 9.9.26. 9. Evaluate C dy y y x dx xy 2 3 2 2 2 3 , where C has 2 segments: 1 2 4 7 5 x x y , from (0,1) to (1,7), and then y = 9 x 2 x 3 from (1,7) to (2,2). 10. Evaluate C dz x xy dy xz xy dx y yz xz 2 2 2 2 where C consists of the two straight line segments from (1,1,0) to (2,3,4) and from (2,3,4) to (2,0,2). Solutions 1 . Zill 9.9.3(a)          14 2 12 0 0 1 2 2 3 2 3 2 , 2 : Check 2 2 : , 2 : 2 , 2 2 28 2 1 4 24 9 2 1 2 9 2 2 1 2 2 1 2 2 1 2 , 3 0 , 1 2 2 1 2 2 1 2 2 1 2 2 1 r F F F d y x y x F y xy x y xy y xy x x y x y x 9.9.3(b) 14 6 8 3 2 3 4 2 1 3 2 2 2 0 1 2 0 2 2 0 2 0 2 , 3 0 , 1 y y dy y dy y y dy y x dx y x dy dx y y x
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ESE 318-02, Fall 2018 2 . Zill 9.9.10(a) 3 5 2 0 1 4 0 1 1 20 sin , 5 sin 2 5 cos cos 5 : , 5 cos : sin 20 , 5 sin 2 0 , 1 0 , 2 3 4 4 2 4 4 2 3 4 r
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