Question: Verify Eq. (11) for the functions in Exercise 44. Data From Exercise 44 A function (x, y, z) is called homogeneous of degree n if

Verify Eq. (11) for the functions in Exercise 44.

af af X  +2 =nf  z af ax

Data From Exercise 44

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) = ln (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x, y, z) = z

af af X +2 =nf z af ax

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