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A1. Consider the system of equations f(x, y, b) = x² − bxy + y² − 1 = 0, g(x, y, b) = x² + y² + b² − 5 = 0 around the point (x, y) = (1,0). Find the point (x, y, b) with b < 0 that satisfies the equations. If b is changed a little to b' = b + db with db = 0.2, what is approximately the new point (r', y', b')? Why is it an approximation?

A1. Consider the system of equations f(x, y, b) = x² − bxy + y² − 1 = 0, g(x, y, b) = x² + y² + b² − 5 = 0 around the point (x, y) = (1,0). Find the point (x, y, b) with b < 0 that satisfies the equations. If b is changed a little to b' = b + db with db = 0.2, what is approximately the new point (r', y', b')? Why is it an approximation?

Advanced Engineering Mathematics
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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A1. Consider the system of equations f(x, y, b) = x² bxy + y² - 1 = 0, g(x, y, b) = x² + y² + b² - 5 = 0 around the point (x, y) = (1,0). Find the point (x, y, b) with b < 0 that satisfies the equations. If b is changed a little to b' = b + db with db = 0.2, what is approximately the new point (x', y', b')? Why is it an approximation?
Transcribed Image Text:A1. Consider the system of equations f(x, y, b) = x² bxy + y² - 1 = 0, g(x, y, b) = x² + y² + b² - 5 = 0 around the point (x, y) = (1,0). Find the point (x, y, b) with b < 0 that satisfies the equations. If b is changed a little to b' = b + db with db = 0.2, what is approximately the new point (x', y', b')? Why is it an approximation?
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