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 fxy f x y x f(x,y) = – x 2 –y 2 2 Set 1 (, 1 ) 1 2 2 y fx x f x x f y y =− − =− Example x 2 2 Volume of a cone (, ) 3 2 3 3 rh Vrh Vr h r h π = = = Example 2 21 2 2 2 22 2 ( ) 2( ) 1 () 0( ) 1 x x x y xy x y x xx y f xy x xx y yx y == + + ∂⋅ + = ∂+ + + = Explaining f/ y 2 2 2 2 2 2 3 (3, ) 3 3 (3 ) x x y y x y fy y f yy = + = +
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Problem 13 on page 517 23 3 22 (, ) l n ( 1 3 ) 1 6 13 1 9 fxy xy f xy xx y f yx y =+ =⋅ ∂+ Problem 17 2 2 2 (, ) 2 fxy x e f ex y x f xe x y = Higher order partials 232 2 32 2 2 2 (, ) 4 5 1 2 8 5 24 15 24 8 24 30 24 15 48 x x y ff x y xy xy x y y x yy y =− + ∂∂ + = + = + + = Problem 25 2 2323 44 () = ()() 2 2 x fx y x y f x y x y y x y fy y y f
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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

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