3.6 Practice Prelim Answers - Review Problems for Prelim 3...

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Unformatted text preview: Review Problems for Prelim 3 Solutions to Partial Derivatives 1. f/x = (1 / 2)( x- y 2 )- 1 / 2 , f/y = (1 / 2)( x- y 2 )- 1 / 2 (- 2 y ) 2. f/x = 3(3 + 2 xy 2 ) 2 (2 y 2 ), f/y = 3(3 + 2 xy 2 ) 2 (4 xy ) 3. f/x = 2 x x 2 + y 3 , f/y = 3 y 2 x 2 + y 3 4. f/x = 2 xy 3 e x 2 y , f/y = 2 ye x 2 y + x 2 y 2 e x 2 y 5. f/x = 2 xy ( x 2 + y 2 )- x 2 y (2 x ) ( x 2 + y 2 ) 2 , f/y = x 2 ( x 2 + y 2 )- x 2 y (2 y ) ( x 2 + y 2 ) 2 6. fx = 4 x 3 + 2 xy 2 + y 3 2 f/x 2 = 12 x 2 + 2 y 2 , 2 f/yx = 4 xy + 3 y 2 7. fx = 1 y + y x 2 2 f/x 2 =- 2 y x 3 , 2 f/yx =- 1 y 2 + 1 x 2 8. fx = ( 1- y x ) e y/x 2 f/x 2 = y x 2 e y/x- y x 2 ( 1- y x ) e y/x , 2 f/yx =- 1 x e y/x + 1 x ( 1- y x ) e y/x Solutions to Definite Integrals (includes Improper Integrals) 9. 25 4 1 x dx = 2 x 1 / 2 25 4 = 10- 4 = 6 10. Let u = 1 + x , du = dx , x (1 + x )- 5 / 2 dx = 1 (1- u ) u- 5...
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3.6 Practice Prelim Answers - Review Problems for Prelim 3...

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