12 - Find an upper bound for the error |E(x, y)|in the standart linear approximation of f(x, y) = x² + y² over the rectangle R: | – 1|<0.2, |y – 2| < 0.1. Use the estimation formula given below. The Error in the Standard Linear Approximation If f has continuous first and second partial derivatives throughout an open set containing a rectangle R centered at (xo, yo) and if M is any upper bound for the values of|f|,|fyl, and |fy| on R, then the error E(x, y) incurred in replacing f(x, y) on R by its linearization L(x, y) = f(xo, yo) + f.(xo. yo)(x – xo) + f,(xo, yo)(v – yo) satisfies the inequality |E(x, y)| < M(|x – xol + ]y – yol)°. a) O |E(x, y)| < 0.15 b) O JE(x,y)| < 0.5 c) O |E(x, y)| < 0.3 |E(x,y)| < 0.06 d) O e) O JE(x, y)| < 0.09

12 - Find an upper bound for the error |E(x, y)|in the standart linear approximation of f(x, y) = x² + y² over the rectangle R: | – 1|<0.2, |y – 2| < 0.1. Use the estimation formula given below. The Error in the Standard Linear Approximation If f has continuous first and second partial derivatives throughout an open set containing a rectangle R centered at (xo, yo) and if M is any upper bound for the values of|f|,|fyl, and |fy| on R, then the error E(x, y) incurred in replacing f(x, y) on R by its linearization L(x, y) = f(xo, yo) + f.(xo. yo)(x – xo) + f,(xo, yo)(v – yo) satisfies the inequality |E(x, y)| < M(|x – xol + ]y – yol)°. a) O |E(x, y)| < 0.15 b) O JE(x,y)| < 0.5 c) O |E(x, y)| < 0.3 |E(x,y)| < 0.06 d) O e) O JE(x, y)| < 0.09

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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