4.2 Class Notes - April 19 Prelim 3 on Tuesday April 24 covers 7.4 Definite integrals 8.2 Volumes 8.4 Improper Integrals 8.1 Integration by parts Ch 11

4.2 Class Notes - April 19 Prelim 3 on Tuesday April 24...

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April 19 Prelim 3 on Tuesday April 24 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 Blackboard Partial Derivatives 2 2 2 2 2 2 2 2 ( , ) 4 7 3 4 0 2 3 0 0 7 0 3 2 2 2 3 f x y x y x xy y f x y x f x y y f f x y f f y x x y = + + = + + = + + = = − = − = ∂ ∂ ∂ ∂ Meaning of partial erivatives 2 2 2 rate of change of when is fixed second derivative w.r.t. when is fixed rate of change of when changes rate of change of when y changes f x y x f x y x f x x f f y x x = = = = ∂ ∂ Partial Derivatives 2 2 2 2 2 2 2 2 ( , ) 4 7 3 ( ,2) 10 2 2 2 (1, ) 5 4 4 2 at 1, 2 0, 0 curve is flat 2 2 neither min nor max f x y x y x xy y f f x x x x x f f y y y y y f f x y x y f f x y = + + = + = − + = + = = = = = = = − f(x,y) = 4x + 7y + x 2 – 3xy – y 2 saddle surface

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