Find the linear approximation of the function f(x, y, z) = √(x^2 + y^2 + z^2) at (2, 4, 4) and u

Step 1: Find the partial derivatives of the function f(x, y, z) = x^2 + y^2 + z^2 with respect t

Question

Find the linear approximation of the function $f(x, y, z) = \sqrt{x^2 + y^2 + z^2}$ at $(2, 4, 4)$ and use it to approximate the number $\sqrt{2.02^2 + 3.97^2 + 3.99^2}$. (Round your answer to five decimal places.) $f(2.02, 3.97, 3.99) \approx$

          Find the linear approximation of the function $f(x, y, z) = \sqrt{x^2 + y^2 + z^2}$ at $(2, 4, 4)$ and use it to approximate the number $\sqrt{2.02^2 + 3.97^2 + 3.99^2}$. (Round your answer to five decimal places.)
$f(2.02, 3.97, 3.99) \approx$

Find the linear approximation of the function f(x, y, z) = √(x^2 + y^2 + z^2) at (2, 4, 4) and use it to approximate the number √(2.02^2 + 3.97^2 + 3.99^2). (Round your answer to five decimal places.)
f(2.02, 3.97, 3.99) ≈

Added by Michael M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Taran S

03/31/2022

Step 1

The partial derivative with respect to x is: ∂f/∂x = 2x The partial derivative with respect to y is: ∂f/∂y = 2y The partial derivative with respect to z is: ∂f/∂z = 2z Show more…

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Find the linear approximation of the function f(, y, z) = /2 + y2 + z2 at (2, 4, 4) and use it to approximate the number /2.022 + 3.972 + 3.992. (Round your answer to five decimal places.) f(2.02,3.97,3.99)