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Given a function f(x, y) of two variables and a constraint g(x, y) = 0, define the following functions of three variables: (a) L₁(x, y, λ) = f(x, y) + g(x, y) — X, (b) L₂(x, y, A) = \f(x, y) + \g(x, y), (c) L3(x, y, λ) = f(x, y) — λg(x, y). Is any one of the equations* VL; (x, y, λ) = 0, j = 1, 2, 3 equivalent to the Lagrange multiplier equations Vf(x, y) = XVg(x, y), g(x, y) = 0? *VL, (x, y, λ) = ( L (x, y, X), y(x, y, λ), (x, y, \)) \)

Given a function f(x, y) of two variables and a constraint g(x, y) = 0, define the following functions of three variables: (a) L₁(x, y, λ) = f(x, y) + g(x, y) — X, (b) L₂(x, y, A) = \f(x, y) + \g(x, y), (c) L3(x, y, λ) = f(x, y) — λg(x, y). Is any one of the equations* VL; (x, y, λ) = 0, j = 1, 2, 3 equivalent to the Lagrange multiplier equations Vf(x, y) = XVg(x, y), g(x, y) = 0? *VL, (x, y, λ) = ( L (x, y, X), y(x, y, λ), (x, y, \)) \)

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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Multiple Choice Given a function f(x, y) of two variables and a constraint g(x, y) = 0, define the following functions of three variables: (a) L₁(x, y, λ) = f(x, y) + g(x, y) — X, (b) L₂(x, y, A) = \ƒ(x, y) + λg(x, y), (c) L3(x, y, λ) = f(x, y) - g(x, y). Is any one of the equations* VL₁(x, y, λ) = 0, j = 1, 2, 3 equivalent to the Lagrange multiplier equations Vf(x, y) = \Vg(x, y), g(x,y)=0 ? ƏLj ; *VL; (x, y, \) = ( ™¹₂¹ (x, y, λ), y (x, y, λ), (x, y, x)) X; əx ду A (a) B (b) C (c) D None of the above I don't know
Transcribed Image Text:Multiple Choice Given a function f(x, y) of two variables and a constraint g(x, y) = 0, define the following functions of three variables: (a) L₁(x, y, λ) = f(x, y) + g(x, y) — X, (b) L₂(x, y, A) = \ƒ(x, y) + λg(x, y), (c) L3(x, y, λ) = f(x, y) - g(x, y). Is any one of the equations* VL₁(x, y, λ) = 0, j = 1, 2, 3 equivalent to the Lagrange multiplier equations Vf(x, y) = \Vg(x, y), g(x,y)=0 ? ƏLj ; *VL; (x, y, \) = ( ™¹₂¹ (x, y, λ), y (x, y, λ), (x, y, x)) X; əx ду A (a) B (b) C (c) D None of the above I don't know
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