14 - Using the definition below, find the linear aproximation of f(x, y) = In(xy²)+ x²yat P(1, 1, 1).DEFINITIONSLinearization, Standard Linear ApproximationThe linearization of a function f(x, y) at a point (xo, yo) where f is differentiableis the functionL(x, y) = f(xo, yo) + f.(xo, yo)(x – xo) + f,(xo, yo)(y – yo).(5)The approximationf(x, y) = L(x, y)is the standard linear approximation of f at (xo, yo).a) O L(x, y)b) O L(x, y) = x + 3y – 6= 3x + y + 5|c) O L(x, y) = x +y – 2d) O L(x, y) = 3x + 3y – 5e) O L(x, y) = 5x + 4y – 3

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14 - Using the definition below, find the linear aproximation of f(x, y) In(xy") + x¯yat. DEFINITIONS Linearization, Standard Linear Approximation The linearization of a function f(x, y) at a point (xo, yo) where ƒ is differentiable is the function L(x, y) = f(xo, yo) + f,(xo, Yo)(x – xo) + f,(xo, yo)(y – yo). (5) The approximation f(x, y) = L(x, y) is the standard linear approximation of f at (xo, yo). a) O L(x, y) = 3x + y + 5 b) O L(x, y) = x + 3y – 6 c) O L(x, y) = x + y – 2 d) O L(x, y) = 3x + 3y – 5 e) O L(г, у) — 5х + 4у — 3 %3D - -

14 - Using the definition below, find the linear aproximation of f(x, y) In(xy") + x¯yat. DEFINITIONS Linearization, Standard Linear Approximation The linearization of a function f(x, y) at a point (xo, yo) where ƒ is differentiable is the function L(x, y) = f(xo, yo) + f,(xo, Yo)(x – xo) + f,(xo, yo)(y – yo). (5) The approximation f(x, y) = L(x, y) is the standard linear approximation of f at (xo, yo). a) O L(x, y) = 3x + y + 5 b) O L(x, y) = x + 3y – 6 c) O L(x, y) = x + y – 2 d) O L(x, y) = 3x + 3y – 5 e) O L(г, у) — 5х + 4у — 3 %3D - -

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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