Answer to Mid-term Review exercises

Answer to Mid-term Review exercises - 2007 1P247249 1 2 3 4...

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Unformatted text preview: 2007 1P247249 1 2 3 4 2P252 4.3 (A)()1 A 4 C D (B)1(5) ) 2 3 ( 2 ) 2 3 ln( 2 ) 2 3 ( 3 ) 2 3 ln( 2 2 2 3 2 2 2 2 y x y x y y x x y z y x y x y y x x x z---- = - +- = 3(1) xy xyz xyz xz y z xy xyz xyz yz x z-- = -- = 2 2 2 2 (2) 1 1 1 1- = - = z z e y z e x z (3) xy xz y z xy yz x z-- = -- = 1 1 1 1 4(2) xy x y y x xy xe e xe e ye ye dx dy- +-- = (3) xy y e y dx dy x 2 cos 2-- = (4) x xy x y xy y dx dy 2 2 2 2 2 2 + + + +- = 3P250251 5 6 4P255 2 3 P264 2 5P260 4.4 (A)()1 B 3 D 4 A C (B)1(1) 1 1 ) 1 , 1 ( 6 27 ) 1 , 1 ( 9 ) , ( 6 , 3 , 6 1 1 3 3 , 3 3 2 2 2 2 2 2 2- = = <- = = = =- = = = = =- = =- = f A D D y y f C y x f B x x f A x y y f y x x f (6) 27 1 ) 3 1 , 3 1 ( 3 2 3 1 ) 3 1 , 3 1 ( 1 ) , 1 ( ) 1 , ( ) , ( 2 , 2 2 1 , 2 ) , 1 ( ) 1 , ( 3 1 3 1 2 , 2 2 2 2 2 2 2 2 = <- = <- = = = =- = =-- = =- = = =-- = =-- = f A D D D D x y f C y x y x f B y x f A x xy x y f y xy y x f 3 3 3 2 2 2 2 2 2 2 2 2 ) 2 ( 2 2 2 ) , , , ( 2 2 2 2 ) , , ( , = = = =- = = + + = = + + = = + + = - + + + = =- + + = z y x xyz F xy y x z F xy z x y F yz z y x F xyz xz yz xy z y x F xyz xz yz xy z y x f z y x 6P266 4.5 (B)1(2) 2 2 2 2 4 ) 2 , 2 ( ) 2 , 2 ) , ( , , 2 1 1 1 ) 1 1 1 ( ) , , ( a a a f a a xy y x f a y x a y x a y x F y x y F x y x F a y x xy y x F = =...
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Answer to Mid-term Review exercises - 2007 1P247249 1 2 3 4...

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