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Suppose 2z³ – 2yz + x = 1 determines the function z = z(x, y) as a function of x, y locally at (x, y, z) = (1,1,1). (a) (a) Find the linear approximation of z at (x, y, z) = (1,1,1). (b) (b) Find the quadratic surface approximation of z at (x, y, z) = (1, 1, 1).

Suppose 2z³ – 2yz + x = 1 determines the function z = z(x, y) as a function of x, y locally at (x, y, z) = (1,1,1). (a) (a) Find the linear approximation of z at (x, y, z) = (1,1,1). (b) (b) Find the quadratic surface approximation of z at (x, y, z) = (1, 1, 1).

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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Suppose 2z³ – 2yz + x = 1 determines the function z = z(x, y) as a function of x, y locally at (x, y, z) = (1,1,1). (a) (a) Find the linear approximation of z at (x, y, z) = (1,1,1). (b) (b) Find the quadratic surface approximation of z at (x, y, z) = (1, 1, 1).
Transcribed Image Text:Suppose 2z³ – 2yz + x = 1 determines the function z = z(x, y) as a function of x, y locally at (x, y, z) = (1,1,1). (a) (a) Find the linear approximation of z at (x, y, z) = (1,1,1). (b) (b) Find the quadratic surface approximation of z at (x, y, z) = (1, 1, 1).
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