A function (x, y, z) is called homogeneous of degree n if (x, y, z) = n

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A function ƒ(x, y, z) is called homogeneous of degree n if ƒ(λx, λy, λz) = λn ƒ(x, y, z) for all λ ∈ R.

Show that the following functions are homogeneous and determine their degree:

(a) f(x, y, z) = xy + xyz (c) f(x, y, z) = In (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x,y, z)= z.4

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 16, 2024 09:01 AM

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A function (x, y, z) is called homogeneous of degree n if (x, y, z) = n

Question:

(a) f(x, y, z) = xy + xyz (c) f(x, y, z) = ln (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x, y, z) = z

Step by Step Answer:

a For fx y z xy xyz we have Ax Ay Az Ax Ay AxAyAz Xxy Xxyz Xxy xyz 1 x y z Hence f i...View the full answer

Calculus

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