hwsol_25 (1)

hwsol_25 (1) - "" dt...

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Homework Assignment 25 - (14.2) - Solutions Page 1120: 10*, 12*, 18*, 21, 27*, 32*, 37*, 39* 10. C : r ! ! t " "# 2 $ t ,3 t % ,0 ! t ! 1, r ! ! t " "# 1,3 % , dy " 3 dt " C 3 y 2 dy " " 0 1 3 ! 3 t " 2 ! 3 dt " " 81 " 0 1 t 2 dt " 27 12. C : r ! ! t " "# 3cos t , 3sin t % ,0 ! t ! ! 2 , r ! ! t " "# # 3sin t , 3cos t % , ds " 9sin 2 t $ 9cos 2 t dt " 3 dt " C ! 3 x # y " ds " " 0 ! /2 ! 3 ! 3cos t " # 3sin t "! 3 dt " " 3 " 0 ! /2 ! 9cos t # 3sin t " dt " 18 18. C : r ! ! t " "# # 2 $ 4 t ,4 % ,0 ! t ! 1, r ! ! t " "# 4,0 % , ds " 4 2 $ 0 dt " 4 dt " C 2 xds " " 0 1 2 ! # 2 $ 4 t "! 4 dt " " 8 " 0 1 ! # 2 $ 4 t " dt " 0 21. C : x " y 2 ,1 ! y ! 2, dx " 2 ydy " C 3 ydx " " 1 2 3 y ! 2 y " dy " " 1 2 6 y 2 dy " 14 27. C : r ! ! x " "# x , x 2 ,2 % ,1 ! x ! 2, r ! ! x " "# 1,2 x ,0 % " C 4 ! x # z " zdx " " 1 2 4 ! x # 2 " 2 dx " # 4 32. C : r ! ! t " "# 3cos t , 3sin t % , t is from ! to 0, r ! ! t " "# # 3sin t , 3cos t % " C F ! # dr ! " " ! 0 # 2 ! 3sin t " , # 2 ! 3cos t " % # # # 3sin t , 3cos t % dt " " ! 0 # 18sin 2 t # 18cos 2 t dt " # 18 " ! 0 dt " 18 ! 37. C " C 1 $ C 2 $ C 3 C 1 : r ! 1 ! t " "# 2 t , t ,2 t % ,0 ! t ! 1, r ! 1 ! t " "# 2,1,2 % C 2 : r ! 2 ! t " "# 2,1,2 # 2 t % ,0 ! t ! 1, r ! 2 ! t " "# 0,0, # 2 % C 3 : r ! 3 ! t " "# 2 # 2 t ,1 # t ,0 % ,0 ! t ! 1, r ! 3 ! t " "# # 2, # 1,0 % " C F ! # dr ! " " C 1 F ! # dr ! $ " C 2 F ! # dr ! $ " C 3 F ! # dr ! " " 0 1 ! # t ,0,2 t % # # 2,1,2 %$# 1,0,2 # 2 t % # # 0,0, # 2 %$# 1 # t ,0,0 % # # # 2, # 1,0 % " dt " " 0 1 ! 2 t $ 4 t $ 4 t # 2 ! 1 # t
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Unformatted text preview: "" dt " 4 39. C : r ! ! t " "# cos t , sin t , 2 t % , 0 ! t ! ! , r ! & ! t " "# # sin t , cos t , 2 % 1 When 2 t " 0, t " 0, when 2 t " ! , t " ! 2 . " C F ! # dr ! " " ! /2 # cos t sin t , 3 ! 2 t " , 1 % # # # sin t , cos t , 2 % dt " " ! /2 # cos t sin 2 t $ 6 t cos t $ 2 dt " # 19 3 $ 4 ! 2...
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hwsol_25 (1) - "" dt...

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