Find the linear approximation of the function f(x, y, z) = x^2 + y^2 + z^2 at (8, 4, 8) and use it to approximate the number 8.03^2 + 3.99^2 + 7.98^2. (Round your answer to five decimal places.) f(8.03, 3.99, 7.98) ≈
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Given: f(x, y, z) = x^2 + y^2 + z^2 Point (x, y, z) = (8, 4, 8) Calculate the partial derivatives: fx = 2x = 2(8) = 16 fy = 2y = 2(4) = 8 fz = 2z = 2(8) = 16 Calculate f(8, 4, 8): f(8, 4, 8) = 8^2 + 4^2 + 8^2 = 64 + 16 + 64 = 144 The linear approximation L(x, Show more…
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