Let X be an open set in Rn. A function F: X R is said to be homogeneous of degree d if

Chapter 2, Problem 41

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Let X be an open set in Rn. A function F: X R is said to be homogeneous of degree d if, for all x = (x1, x2,..., xn) X and all t R such that tx X, we have F(t x1, t x2,..., t xn) = t d F(x1, x2,..., xn). Exercises 3744 concern homogeneous functions. In Exercises 3741, which of the given functions are homogeneous? For those that are, indicate the degree d of homogeneity.F(x, y,z) = x 3 + x 2 y yz2 xyz + 7x z2