hwsol_8 - Homework Assignment 8- (11.2) - Solutions Page...

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Homework Assignment 8- (11.2) - Solutions Page 871: 6, 8*, 10*, 12*, 14, 16*, 18*, 21*, 22*, 24*, 25*, 30*, 31*, 32*, 36*, 38*, 40*, 43, 46*, 52* 6. lim t ! 1 " t 2 , e 2 t , t 2 # 2 t $%" 1, e 2 ,3 $ 8. lim t ! 1 " t ! 1 , t 2 # 3, t # 1 t ! 1 $%" 0, 4, DNE $ DNE 10. lim t ! ! /2 " cos t , t 2 # 3, tan t $%" 0, ! 2 4 # 3, DNE $ DNE 12. r & ! t " %" sin t , cos t , 3 t $ Both sin t and cos t are continuous everywhere. 3 t are continuous if t " 0. r & ! t " is continuous everywhere except t % 0. 14. r & ! t " %" cos5 t , tan t , 6sin t $ Both sin t and cos t are continuous everywhere. tan t is continuous wherever cos t " 0. So, r & ! t " is continuous everywhere except when t % ! 2 n ! , n % 0,1,. .. 16. r & ! t " %" sin t , ! csc t , cot t $ Both csc t and cot t are continuous everywhere except where sin t % 0. So, r & ! t " is continuous everywhere except when t %’ n ! , n % 18. r & ! t " %" t ! 3 t # 1 , te 2 t , t 3 $ , r & ( ! t " %" t # 1 ! t # 3 ! t # 1 " 2 , e 2 t # 2 te 2 t t 2 $%" 4 ! t # 1 " 2 , e 2 t ! 1 # 2 t " t 2 $ 21. r & ! t " %" e t 2 , t 2 , sec ! 2 t " $ , r & ( ! t " %" 2 te t 2 ,2 t , 2sec ! 2 t " tan ! 2 t " $ 22. r & ! t " %" t 2 # 1 , cos t , e ! 3 t $ , r & ( ! t " %" t t 2 # 1 , ! sin t , ! 3 e ! 3 t $ 24. r & ! t " %" t , t 2 ! 1 $ , t % 0,1,2 r & ! 0 " %" 0, ! 1 $ , r & ! 1 " %" 1, 0 $ , r & ! 2 " %" 2, 3 $ r & ( ! t " %" 1, 2 t $ , r & ( ! 0 " %" 1, 0 $ , r & ( ! 1 " %" 1,2 $ , r & ( ! 2 " %" 1, 4 $ 1
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0 2 4 6 8 -3 -2 -1 1 2 3 25. r & ! t " %" cos t , t , sin t $ , t % 0, t % ! 2 , t % ! r & ! 0 " %" 1, 0, 0 $ , r & ! 2 %" 0, ! 2 ,1 $ , r & ! ! " %" ! 1, ! ,0 $ r & ( ! t " %" ! sin t , 1, cos t $ , r & ( ! 0 " %" 0,1,1 $ , r & ( ! 2 %" ! 1, 1, 0 $ , r & ( ! ! " %" 0, 1, ! 1 $ -1 -0.5 0 0.5 1 2 4 6 y -1 -0.5 0.5 1 t 30. # " e ! 3 t , sin5 t , t 3/2 $ dt %" ! 1 3 e ! 3 t , ! 1 5 cos5 t , 2 5 t 5/2 $# C & 31. # " te t 2 ,3 t sin t , 3 t t 2 # 1 $ dt %" 1 2 e t 2 , 3sin t ! 3 t cos t , 3 2 ln ! t 2 # 1 " C & 32. # " e ! 3 t , t 2 cos t 3 , t cos t $ dt %" ! 1 3 e ! 3 t , ! 1 3 sin t 3 , cos t # t sin t C & 2
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36. # 0 4 " 2 te 4 t , t 2 ! 1, 4 t t 2 # 1 $ dt : %" 1 2 te 4 t ! 1 8 e 4 t , 1 3 t 3 ! t ,2 l n ! t 2 # 1 " $ | 0 4 %" 15 8 e 16 # 1 8 , 52 3 , 2ln17 $ 38. r & ! t " %" 2cos t , sin t $ , r & ( ! t " %" ! 2sin t , cos t $ r & ! t " # r & ( ! t " % ! 4sin t cos t # sin t cos t % ! 3sin t cos t % ! 3 2 sin ! 2 t " % 0 2 t % n ! , n % 0, 1,. .., t % 1 2 n ! , n % 0, 1, 2, . .. 40. r & ! t " %" t 2 , t , t 2 ! 5 $ , r & ( ! t " %" 2 t ,1 t $ r & ! t " # r & ( ! t " % 2 t 3 # t # 2 t 3 ! 10 t % 4 t 3 ! 9 t % t ! 4 t 2 ! 9 " % 0, t % 0, t %’ 3 2 43. r & ! t " %" t , t , t 3 ! 3 $ , r & ( ! t " %" 1, 1, 3 t 2 $ ,3 t 2 % 0, t % 0.
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hwsol_8 - Homework Assignment 8- (11.2) - Solutions Page...

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