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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:12 - Find an upper bound for the error |E(x, y)| in the standart linear approximation of f(x, y) = x² + y? over the
rectangle R: |x – 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 |fry| 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)(y – yo)
satisfies the inequality
|E(x, y)| < M(\x – xol + ly – yol).
a) O |E(x, y)| < 0.15
b) O |E(x,y)| < 0.5
c) O |E(x, y)| < 0.3
d) O E(x, y)| < 0.06
e) O |E(x, y)| < 0.09
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