hwsol_24

hwsol_24 - x 2 y % C ! y , z " f y ! $ $ y ! z...

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Homework Assignment 24 - (14.1) - Solutions Page 1106: 8*, 10* - for both problem choose: x,y ! -2,-1,0,1,2 15, 42*, 44*, 20*, 26* - for both 20 and 26 without graphing, 34*, 36* 8. F " ! x , y " !# 2 x ,0 $ 10. F " ! x , y " !# ! 1, y 2 $ -2 -1 0 1 2 -2 -1 1 2 x 8. F " ! x , y " !# 2 x ,0 $ -2 -1 0 1 2 y -2 -1 1 2 x 10. F " ! x , y " !# ! 1, y 2 $ 42. F " ! x , y " !# 1 y ,2 x $ dx dt ! 1 y dy dt ! 2 x # dx dy ! 1 y 1 2 x # 2 xdx ! 1 y dy # " 2 xdx ! " 1 y dy # x 2 ! ln| y | % C 44. F " ! x , y " !# e ! x ,2 x $ dx dt ! e ! x dy dt ! 2 x # dx dy ! e ! x 2 x ! 1 2 xe x # 2 xe x dx ! dy # " 2 xe x dx ! " dy 2 xe x ! 2 e x ! y % C , y ! 2 xe x ! 2 e x % C 20. f ! x , y " ! sin ! x 2 % y 2 " F " ! x , y " ! # f ! x , y " !# 2 x cos ! x 2 % y 2 " ,2 y cos ! x 2 % y 2 " $ 26. f ! x , y , z " ! ! x ! y " 2 % z F " ! x , y , z " !# 2 ! x ! y " , ! 2 ! x ! y " ,1 $ 34. F " ! x , y " !# y cos x , sin x ! y $ . Determine if it is possible to fine f ! x , y " such that # f ! F " . f x ! y cos x , f ! x , y " ! " y cos xdx ! y sin x % C ! y " f y ! $ $ y ! y sin x % C ! y "" ! sin x % C ! y " ! sin x ! y , C ! y " ! ! y , C ! y " ! " ! ydy ! ! 1 2 y 2 % C 1
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f ! x , y " ! y sin x ! 1 2 y 2 % C So, F " is conservative. 36. F " ! x , y , " !# z 2 % 2 xy , x 2 ! z ,2 xz ! 1 $ . Determine if it is possible to fine f ! x , y , z " such that # f ! F " . f x ! z 2 % 2 xy , f ! x , y , z " ! " ! z 2 % 2 xy " dx ! z 2 x %
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Unformatted text preview: x 2 y % C ! y , z " f y ! $ $ y ! z 2 x % x 2 y % C ! y , z "" ! x 2 % C y ! y , z " ! x 2 ! z , C y ! y , z " ! ! z , C ! y , z " ! " ! zdy ! ! zy % C ! z " , f ! x , y , z " ! z 2 x % x 2 y ! zy % C ! z " f z ! 2 zx ! y % C & ! z " ! 2 xz ! 1, C & ! z " ! y ! 1 - contradict to C & ! z " is a function of z only So, F " does not have a potential function and it is not conservative. 2...
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hwsol_24 - x 2 y % C ! y , z " f y ! $ $ y ! z...

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