quiz3_sol - df = 1 3 dx + 2 dy 3. (3pts.) Use part 2. to...

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Date: Feb 02, 2011 MA3160-08 Quiz 3 Justify all answers! Name (print): Solutions Let f ( x , y ) = p x 2 + y 3 . 1. (3pts.) Use a di erence quotient to approximate f x (1 , 0) with h = 0 . 1. The di erence quotient corresponding to f x (1 , 0) is f (1 + h , 0) - f (1 , 0) h = 1 . 1 2 + 0 3 - 1 2 + 0 3 0 . 1 = 1 . 1 - 1 0 . 1 = 1 2. (4pts.) Find the di erential of f ( x , y ) at the point (1,2). Note that f x ( x , y ) = x p x 2 + y 3 and f y ( x , y ) = 3 y 2 2 p x 2 + y 3 Therefore, df = f x ( x , y ) dx + f y ( x , y ) dy = x p x 2 + y 3 dx + 3 y 2 2 p x 2 + y 3 dy and at the point (1,2)
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Unformatted text preview: df = 1 3 dx + 2 dy 3. (3pts.) Use part 2. to estimate f (1 . 1 , 1 . 9). f (1 . 1 , 1 . 9) ≈ f (1 , 2) + f x (1 , 2) Δ x + f y (1 , 2) Δ y = 3 + 1 3 (0 . 1) + 2(-. 1) Therefore, f (1 . 1 , 1 . 9) ≈ 2 5 6 ≈ 2 . 833...
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This note was uploaded on 04/04/2011 for the course MA 3160 taught by Professor Staff during the Spring '08 term at Michigan Technological University.

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