4.1 Class Notes - April 17 Prelim 3 a week from today covers 7.4 Definite integrals 8.2 Volumes 8.4 Improper Integrals 8.1 Integration by parts Ch 11

4.1 Class Notes - April 17 Prelim 3 a week from today...

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April 17 Prelim 3 a week from today covers 7.4 Definite integrals 8.2 Volumes, 8.4 Improper Integrals 8.1 Integration by parts Ch. 11. Probability distributions 9.2 Partial derivatives i.e., the material from HWK 7,8,9 Formula and review sheets on Blackboad Partial Derivatives Given ( , ) the partial derviative is computed by holding constant and differentiating the resulting function of f x y f x y x f(x,y) = – x 2 – y 2 2 Set 1 ( , 1) 1 2 2 y f x x f x x f y y = − = = − = − Example x 2 2 Volume of a cone ( , ) 3 2 3 3 r h V r h V rh r V r h π π π = = = Example 2 2 1 2 2 2 2 2 2 ( , ) ( ) 2 ( ) 1 ( ) 0 ( ) 1 ( ) ( ) x f x y x x y x y f x x y x x x y f x y x x x y y x y = = + + + = + + = − + = + Explaining f/ y 2 2 2 2 2 2 ( , ) ( ) 3 (3, ) 3 3 (3 ) x f x y x y f x y x y f y y f y y = + = − + = + = − +
Problem 13 on page 517 2 3 3 2 3 2 2 2 3 ( , ) ln(1 3 ) 1 6 1 3 1 9 1 3 f x y x y f xy x x y f x y y x y = + = + = + Problem 17 2 2 2 2 2 ( , ) 2 x y x y x y x y f x y xe f e xe xy x f xe x y = = + = Higher order partials 2 3 2 2 3 2 2 2 2 2 2 ( , ) 4 5 12 8 5 24 15 24 8 24 30 24 15 48 f x y x xy x y f f x y xy xy x y x y f f y xy x x x y y f f y xy y x x y = +

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