34BL23 - Math 34B Lecture 23 Copyright Daryl Cooper...

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Unformatted text preview: Math 34B Lecture 23 Copyright Daryl Cooper D.A.R.Y.L. March 8, 2010 I like using iclickers in class ? A = Yes B = No C = prefer not so say Lectures online accessible via webwork. http://www.math.ucsb.edu/ ∼ cooper/34BL23 Δ f = f ( x + Δ x , y + Δ y )- f ( x , y ) ≈ f x ( x , y )Δ x + f y ( x , y )Δ y f ( x , y ) = 2 x 3 + 2 xy + 4 y 2 Use the tangent plane approximation to find an approximate value for Δ f = f (1 . 02 , 1 . 03)- f (1 , 1) A = . 16 B = 0 . 46 C = 4 . 46 D = 0 . 32 Δ f = f ( x + Δ x , y + Δ y )- f ( x , y ) ≈ f x ( x , y )Δ x + f y ( x , y )Δ y f ( x , y ) = 2 x 3 + 2 xy + 4 y 2 Use the tangent plane approximation to find an approximate value for Δ f = f (1 . 02 , 1 . 03)- f (1 , 1) A = . 16 B = 0 . 46 C = 4 . 46 D = 0 . 32 B f x ( x , y ) = 6 x 2 + 2 y so f x (1 , 1) = 6(1) 2 + 2(1) = 8 f y ( x , y ) = 2 x + 8 y so f y ( x , y ) = 2(1) + 8(1) = 10 Δ x = . 02 and Δ y = . 03 so Δ f ≈ (8)(0 . 02) + (10)(0 . 03) = . 16 + . 3 = . 46 Find Δ f = f (1 + Δ x , 1 + Δ y )- f (1 , 1) to first order in Δ x and Δ y . A = Δ x + Δ y B = 8 + Δ x + 10 + Δ y C = 8Δ x + 10Δ y Δ f = f ( x + Δ x , y + Δ y )- f ( x , y ) ≈ f x ( x , y )Δ x + f y ( x , y )Δ y f ( x , y ) = 2 x 3 + 2 xy + 4 y 2 Use the tangent plane approximation to find an approximate value for Δ f = f (1 . 02 , 1 . 03)- f (1 , 1) A = . 16 B = 0 . 46 C = 4 . 46 D = 0 . 32 B f x ( x , y ) = 6 x 2 + 2 y so f x (1 , 1) = 6(1) 2 + 2(1) = 8 f y ( x , y ) = 2 x + 8 y so f y ( x , y ) = 2(1) + 8(1) = 10 Δ x = . 02 and Δ y = . 03 so Δ f ≈ (8)(0 . 02) + (10)(0 . 03) = . 16 + . 3 = . 46 Find Δ f = f (1 + Δ x , 1 + Δ y )- f (1 , 1) to first order in Δ x and Δ y . A = Δ x + Δ y B = 8 + Δ x + 10 + Δ y C = 8Δ x + 10Δ y C f x (1 , 1)Δ x + f y (1 , 1)Δ y = 8 Δ x + 10 Δ y If Δ x = 0 . 1 what approximately should Δ y be so that f does not change ie f (1 + Δ x , 1 + Δ y ) = f (1 , 1)? A =- . 1 B =- . 8 C = 0 . 8 D = 0 . 1 Δ f = f ( x + Δ x , y + Δ y )- f ( x , y ) ≈ f x ( x , y )Δ x + f y ( x , y )Δ y f ( x , y ) = 2 x 3 + 2 xy + 4 y 2 Use the tangent plane approximation to find an approximate value for Δ f = f (1 . 02 , 1 . 03)- f (1 , 1) A = . 16 B = 0 . 46 C = 4 . 46 D = 0 . 32 B f x ( x , y ) = 6 x 2 + 2 y so f x (1 , 1) = 6(1) 2 + 2(1) = 8 f y ( x , y ) = 2 x + 8 y so f y ( x , y ) = 2(1) + 8(1) = 10 Δ x = . 02 and Δ y = . 03 so Δ f ≈ (8)(0 . 02) + (10)(0 . 03) = . 16 + . 3 = . 46 Find Δ f = f (1 + Δ x , 1 + Δ y )- f (1 , 1) to first order in Δ x and Δ y . A = Δ x + Δ y B = 8 + Δ x + 10 + Δ y C = 8Δ x + 10Δ y C f x (1 , 1)Δ x + f y (1 , 1)Δ y = 8 Δ x + 10 Δ y If Δ x = 0 . 1 what approximately should Δ y be so that f does not change ie f (1 + Δ x , 1 + Δ y ) = f (1 , 1)?...
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34BL23 - Math 34B Lecture 23 Copyright Daryl Cooper...

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