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hwsol_10

# hwsol_10 - Homework Assignment 10(11.4 Solutions Page 888 6...

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Homework Assignment 10 - (11.4) - Solutions Page 888: 6*, 7*, 13, 14*, 17, 18*, 20*, 22*, 26*, 30*, 34*, 38*, 40*, 43-46, 50*, 51* 6. r ! ! t " "# 5cos t ,5sin t \$ , r ! % ! t " "# ! 5sin t , 5cos t \$ s ! t " " " 0 t 25sin 2 u & 25sin 2 u du " " 0 t 5 du " 5 u | 0 t " 5 t , t " s 5 , s " 5 t r ! ! s " " # 5cos s 5 , 5sin s 5 \$ , 0 # t # 2 ! # 0 # s # 10 ! 10. r ! ! t " "# 3 t , 4 t \$ , r ! % ! t " "# 3, 4 \$ s ! t " " " 0 t 3 2 & 4 2 du " " 0 t 5 du " 5 t , t " s 5 , s " 5 t r ! ! s " " # 3 5 s , 4 5 s \$ , 0 # t # 1 # 0 # s # 5 13. r ! ! t " "# 3 t , cos2 t , sin2 t \$ , t " 0, ! ! , ! r ! % ! t " "# 3, ! 2sin2 t , 2cos2 t \$ , r ! % ! t " " 9 & 4 " 13 T ! ! t " " 1 13 # 3, ! 2sin2 t , 2cos2 t \$ T ! ! 0 " " 1 13 # 3,0,2 \$ , T ! ! ! ! " " 1 13 # 3, 0, 2 \$ , T ! ! ! " " 1 13 # 3, 0,2 \$ 14. r ! ! t " "# 4 t , 2 t , t 2 \$ , t " ! 1, t " 0, t " 1 r ! % ! t " "# 4, 2, 2 t \$ , r ! % ! t " " 4 2 & 2 2 & ! 2 t " 2 " 2 5 & t 2 T ! ! t " " 1 2 5 & t 2 # 4, 2, 2 t \$" 1 5 & t 2 # 2, 1, t \$ T ! ! ! 1 " " 1 6 # 2, 1, ! 1 \$ , T ! ! 0 " " 1 5 # 2, 1, 0 \$ , T ! ! 1 " " 1 6 # 2, 1, 1 \$ , 17. r ! ! t " "# 3 t , cos2 t , sin2 t \$ r ! ! 0 " "# 0, 1, 0 \$ , r ! ! ! ! " "# ! 3 ! , 1, 0 \$ , r ! ! ! " "# 3 ! , 1, 0 \$ T ! ! 0 " " 1 13 # 3,0,2 \$ , T ! ! ! ! " " 1 13 # 3, 0, 2 \$ , T ! ! ! " " 1 13 # 3, 0, 2 \$ 1

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-1 -0.5 0.5 1 0.5 1 y -10 t ° r ! ! t " , -.-. T ! ! t " 18. r ! ! t " "# 4 t , 2 t , t 2 \$ r ! ! ! 1 " "# ! 4, ! 2, 1 \$ , r ! ! 0 " "# 0,0,0 \$ , r ! ! 1 " "# 4,2,1 \$ T ! ! ! 1 " " 1 6 # 2, 1, ! 1 \$ , T ! ! 0 " " 1 5 # 2, 1, 0 \$ , T ! ! 1 " " 1 6 # 2, 1, 1 \$ , 0 0.5 1 1.5 -4 -2 2 4 y -5 5 t 20. r ! ! t " "# 2, sin ! ! t " , ln ! t " \$ , t " 1 r ! % ! t " "# 0, ! cos ! ! t " , 1 t \$ , r ! % ! 1 " "# 0, ! ! , 1 \$ , r ! % ! 1 " " ! 2 & 1 r ! %% ! t " "# 0, ! ! 2 sin ! ! t " , ! 1 t 2 \$ , r ! %% ! 1 " "# 0, 0, ! 1 \$ r ! % ! 1 " r ! %% ! 1 " " i ! j ! k ! 0 ! ! 1 0 0 ! 1 " ! i ! , r ! % ! 1 " r ! %% ! 1 " " ! 2
" " ! ! 2 & 1 3 " 8. 766561 10 ! 2 22. r !

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hwsol_10 - Homework Assignment 10(11.4 Solutions Page 888 6...

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