Using the first three terms of the Taylor series of z = = f(x,y) about (a, b), we can write f(x,y) – f(a,b) ≈ 41¹ (x − a) – 40º0 (y – b) By measurement, x = 41 with maximum absolute error 0.04, and y = 40 with maximum absolute error 0.02. That is, |x-41 ≤ 0.04 and y-40 ≤ 0.02. Estimate the maximum possible error in the computation of z. Enter your answer to 2 decimal places in the box below.
Using the first three terms of the Taylor series of z = = f(x,y) about (a, b), we can write f(x,y) – f(a,b) ≈ 41¹ (x − a) – 40º0 (y – b) By measurement, x = 41 with maximum absolute error 0.04, and y = 40 with maximum absolute error 0.02. That is, |x-41 ≤ 0.04 and y-40 ≤ 0.02. Estimate the maximum possible error in the computation of z. Enter your answer to 2 decimal places in the box below.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Using the first three terms of the Taylor series of z=f(x,y) about (a,b), we can write
ƒ (x, y) — ƒ (a, b) ≈ 41 (x − a) (y - b)
40
9
By measurement, x = 41 with maximum absolute error 0.04, and y 40 with maximum absolute error 0.02. That is,
|x - 41| ≤ 0.04 and y-40 ≤ 0.02.
Estimate the maximum possible error in the computation of z. Enter your answer to 2 decimal places in the box below.
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