Engineering Calculus Notes 364

Engineering Calculus Notes 364 - a = ( , 3 ) is T 2 f pp ,...

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352 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION We consider two examples. The function f ( x,y ) = e 2 x cos y has ∂f ∂x ( x 0 ,y 0 ) = 2 e 2 x cos y ∂f ∂y ( x 0 ,y 0 ) = e 2 x sin y 2 f 2 x ( x 0 ,y 0 ) = 4 e 2 x cos y 2 f ∂x∂y ( x 0 ,y 0 ) = 2 e 2 x sin y 2 f 2 y ( x 0 ,y 0 ) = e 2 x cos y. At −→ a = ( 0 , π 3 ) , these values are f p 0 , π 3 P = e 0 cos π 3 = 1 2 ∂f ∂x p 0 , π 3 P = 2 e 0 cos π 3 = 1 ∂f ∂y p 0 , π 3 P = e 0 sin π 3 = 3 2 2 f 2 x p 0 , π 3 P = 4 e 0 cos π 3 = 2 2 f ∂x∂y p 0 , π 3 P = 2 e 0 sin π 3 = 3 2 f 2 y p 0 , π 3 P = e 0 cos π 3 = 1 2 so the degree two Taylor polynomial at
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Unformatted text preview: a = ( , 3 ) is T 2 f pp , 3 PP x, y = 1 2 + x 3 2 y + x 2 1 4 y 2 3 x y. Let us compare the value f ( . 1 , 2 ) with f ( , 3 ) = 0 . 5:...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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