Engineering Calculus Notes 261

Engineering Calculus Notes 261 - y 2 r x 2 + 5 xy + y 2 so...

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3.3. DERIVATIVES 249 Approximation and Estimation Just as for functions of one variable, the linearization of a function can be used to get “quick and dirty” estimates of the value of a function when the input is close to one where the exact value is known. For example, consider the function f ( x,y ) = r x 2 + 5 xy + y 2 ; you can check that f (3 , 1) = 5; what is f (2 . 9 , 1 . 2)? We calculate the partial derivatives at (3 , 1): ∂f ∂x ( x,y ) = 2 x + 5 y 2 r x 2 + 5 xy + y 2 ∂f ∂y ( x,y ) = 5 x + 2
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Unformatted text preview: y 2 r x 2 + 5 xy + y 2 so f x (3 , 1) = 11 10 = 1 . 1 f y (3 , 1) = 17 10 = 1 . 7; since (2 . 9 , 1 . 2) = (3 , 1) + ( . 1 , . 2) we use x = . 1 , y = 0 . 2 to calculate the linearization T (3 , 1) f (2 . 9 , 1 . 2) = f (3 , 1) + f x (3 , 1) x + f y (3 , 1) y = 5 + (1 . 1)( . 1) + (1 . 7)(0 . 2) = 5 . 11 + 0 . 34 = 5 . 23 ....
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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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