hwsol_14

# hwsol_14 - sin nc x&amp;quot sin nc y&amp;quot f xx...

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Homework Assignment 14 - (12.3) - Solutions Page 944 : 12*, 16*, 20*, 24*, 28*, 40*, 53* 12. f ! x , y " ! x ! 3 y " x 2 tan y " f ! x , y " " x ! 1 y " 2 x ! tan y " , " f ! x , y " " y ! ! x " 3 y 2 " x 2 ! sec 2 y " 16. f ! x , y , z " ! y x 2 " y 2 " z 2 " f ! x , y , z " " x ! ! yx ! x 2 " y 2 " z 2 " 3 2 , " f ! x , y , z " " y ! x 2 " z 2 ! x 2 " y 2 " z 2 " 3 2 , " f ! x , y , z " " z ! ! yx ! x 2 " y 2 " z 2 " 3 2 20. f ! x , y " ! e 4 x ! sin y 2 ! xy , f ! x , y " ! e 4 x ! sin y 2 ! x y " f ! x , y " " x ! 4 e 4 x ! 1 2 x y , " f ! x , y " " y ! ! 2sin y cos y ! x 1 2 y " 2 f ! x , y " " x 2 ! 16 e 4 x " 1 4 ! x " 3/2 y , " 2 f ! x , y " " x " y ! ! 1 4 x y , " 3 f ! x , y " " x " y " y ! 1 8 x y 3 2 24. f ! x , y , z " ! ln ! xyz 2 " , f ! x , y , z " ! ln x " ln y " 2ln z " f ! x , y " " x ! 1 x , " f ! x , y " " y ! 1 y " 2 f ! x , y " " x 2 ! ! 1 x 2 , " 2 f ! x , y " " y 2 ! ! 1 y 2 , " 3 f ! x , y " " y " y " z ! 0, " 5 f ! x , y " " x " x " y " z " z ! 0 28. f ! x , y " ! x 2 " y 2 , f x ! 1,0 " , The trace: f ! x , y " ! f ! 1,0 " , x 2 " y 2 ! 1, or x 2 " y 2 ! 1 0 0.5 1 1.5 2 2.5 -2 -1 1 2 y -2 -1 1 2 x 0 0.5 1 1.5 -1 -0.5 0.5 1 y -1 -0.5 0.5 1 f x ! x x 2 " y 2 , f x ! 1,0 " ! 1 1

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40. f ! x , y " ! x 2 " y 2 ! x 4 f x ! 2 x ! 4 x 3 ! 2 x ! 1 ! 2 x 2 " ! 0, x ! 0, or x ! # 1 2 f y ! 2 y ! 0, y ! 0 f x ! 0 and f y ! 0 at ! 0,0 " , 1 2 ,0 , ! 1 2 ,0 53. f ! x , y " ! sin ! n ! x " cos ! nc ! y " f x ! n ! cos ! n ! x " cos ! nc ! x " , f y ! ! nc
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Unformatted text preview: ! sin ! nc ! x &amp;quot; sin ! nc ! y &amp;quot; f xx ! ! ! n ! &amp;quot; 2 sin ! n ! x &amp;quot; cos ! nc ! x &amp;quot; , f yy ! ! ! nc ! &amp;quot; 2 sin ! nc ! x &amp;quot; cos ! nc ! y &amp;quot; c 2 f xx ! ! c 2 ! n ! &amp;quot; 2 sin ! n ! x &amp;quot; cos ! nc ! x &amp;quot; ! f yy 2...
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