quiz_02C - f(3 Δ x 2 Δ y 6 Δ z ≈ 7 3 7 Δ x 2 7 Δ y 6...

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Math 213 — Quiz 2 Name 1. Find the linear approximation of the function f ( x,y,z ) = p x 2 + y 2 + z 2 at (3 , 2 , 6) and use it to approximate p (3 . 02) 2 + (1 . 97) 2 + (5 . 99) 2 . The partial derivatives of f are f x ( x,y,z ) = x p x 2 + y 2 + z 2 , f y ( x,y,z ) = y p x 2 + y 2 + z 2 , f z ( x,y,z ) = z p x 2 + y 2 + z 2 . Evaluating f,f x ,f y ,f z at (3 , 2 , 6), we find the linearization
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Unformatted text preview: f (3 + Δ x, 2 + Δ y, 6 + Δ z ) ≈ 7 + 3 7 Δ x + 2 7 Δ y + 6 7 Δ z. Therefore, f (3 . 02 , 1 . 97 , 5 . 99) ≈ 7 + 3 7 (0 . 02) + 2 7 (-. 03) + 6 7 (-. 01) = 7-6 700 ....
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