A function is homogeneous of degree n when (tx, ty) t n (x, y) (a) Show that the function is homogeneous and determine n (b) Show that x x (x, y) y y (x, y) n(x, y) f(x, y) x x y...

A function is homogeneous of degree n when (tx, ty) = t n (x, y). (a)

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A function ƒ is homogeneous of degree n when ƒ(tx, ty) = tⁿƒ(x, y).

(a) Show that the function is homogeneous and determine n

(b) Show that xƒ_x(x, y) + yƒ_y(x, y) = nƒ(x, y).

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Calculus

ISBN: 9781285057095

10th Edition

Authors: Ron Larson, Bruce H. Edwards

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Question Posted: Mar 29, 2023 01:59 AM

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A function is homogeneous of degree n when (tx, ty) = t n (x, y). (a)

Question:

f(x, y) = x² x² + y²

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Calculus

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