Question

Find the linear approximation of the function below at the indicated point. f(x, y) = sqrt{29 - x^2 - 4y^2} at (2, 2) f(x, y) approx Use this approximation to find f(2.07, 1.94). (Round your answer to three decimal places.) f(2.07, 1.94) approx

          Find the linear approximation of the function below at the indicated point.
f(x, y) = sqrt{29 - x^2 - 4y^2} at (2, 2)
f(x, y) approx 
Use this approximation to find f(2.07, 1.94). (Round your answer to three decimal places.)
f(2.07, 1.94) approx

Find the linear approximation of the function below at the indicated point.
f(x, y) = sqrt29 - x^2 - 4y^2 at (2, 2)
f(x, y) approx
Use this approximation to find f(2.07, 1.94). (Round your answer to three decimal places.)
f(2.07, 1.94) approx

Added by Xavier B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/20/2023

Step 1

Given function: \(f(x, y) = 29 - x^2 - 4y^2\) Linear approximation formula: \(L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)\) At point (2, 2): \(f(2, 2) = 29 - 2^2 - 4(2)^2 = 29 - 4 - 16 = 9\) Calculate partial derivatives: \(f_x = -2x\), \(f_y = Show more…

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