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223Exam2review

# 223Exam2review - Math 223 Spring 2008 Dawson Notes for...

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Math 223 Spring 2008 Dawson Notes for Exam #2 The exam covers sections 14.1-14.7 & 16.1-16.4. Extra Problems The best review for your exam is to go over the previously assigned homework problems. If you would like some extra problems to work on, take a look at those listed below. Review Exercises from Chapter 14 - pg 741-746 : #5, 6 (second one should say F y ), 11, 12, 14, 17, 18, 22, 24, 25, 27, 29, 32, 34, 37, 40, 45, 51, 56, 59 Review Exercises from Chapter 16 - pg 825-829 : #2, 3, 5, 10, 11, 13, 14, 17, 26-39, 40, 41, 43 Solutions to above review problems Please let me know if you find any mistakes. Review Exercises from Chapter 14 5. f x ( x, y ) = 2 xy 3 ( x 2 + y 2 ) 2 , f y ( x, y ) = x 4 - x 2 y 2 ( x 2 + y 2 ) 2 6. F r = - 3 Gμmyr ( r 2 + y 2 ) 5 / 2 , F y = Gμm ( r 2 - 2 y 2 ) ( r 2 + y 2 ) 5 / 2 11. x ( e x cos( xy ) + ay 2 ) = e x cos( xy ) - ye x sin( xy ) , y ( e x cos( xy ) + ay 2 ) = - xe x sin( xy ) + 2 ay, a ( e x cos( xy ) + ay 2 ) = y 2 12. πφ cos( πθφ ) + 2 θ θ 2 + φ 14. u xx = e x sin( y ) , u yy = - e x sin( y ) 17. f = (3 x 2 - yz ) i - xzj + (3 z 2 - xy ) k 18. f = cos( y 2 - xy )( - y ) i + cos( y 2 - xy )(2 y - x ) j 22. -1 24. 0 25. 24 19 27. 4 i - 2 j

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29. 2 i - 2 j - 6 k 32. Q ( x, y ) = 1 + 1( x - 3) - 1 2 ( y - 5) - 1 2 ( x - 3) 2 + 1 2 ( x - 3)( y - 5) - 1 8 ( y - 5) 2 34. 1 37. ≈ - . 71 40. 4 2, In the direction of 6 i + 2 j 45. ± 4 2 11 1 2 , - 1 2 , 3 2 51. The derivative
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