Question

Find the linear approximation to the surface $f(x, y) = 2x - xy + 2y$ at $(2, 1)$ and use this to approximate $f(1.9, 0.9)$. (a) 3.80 (b) 3.89 (c) 3.90 (d) 4.11 (e) 4.19

          Find the linear approximation to the surface $f(x, y) = 2x - xy + 2y$ at $(2, 1)$ and use this to approximate $f(1.9, 0.9)$. 
(a) 3.80
(b) 3.89
(c) 3.90
(d) 4.11
(e) 4.19

Added by Leroy C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Abigail Martyr

07/06/2020

Step 1

f(x,y) = 2x - xy + 2y ∂f/∂x = 2 - y ∂f/∂y = -x + 2 Next, we evaluate these partial derivatives at the point (2,1): ∂f/∂x at (2,1) = 2 - 1 = 1 ∂f/∂y at (2,1) = -2 + 2 = 0 The linear approximation at (2,1) is given by: L(x,y) = f(2,1) + ∂f/∂x(2,1)(x-2) + Show more…

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Find the linear approximation to the surface f(x,y)=2x-xy+2y at (2,1) and use this to approximate f(1.9,0.9). (a) 3.80 (b) 3.89 (c) 3.90 (d) 4.11 (e) 4.19 Find the linear approximation to the surface f(x,y) = 2x xy + 2y at (2,1) and use this to approximate f(1.9,0.9) (a) 3.80 (b) 3.89 (c) 3.90 (d) 4.11 (e) 4.19