please send handwritten solution for 3.19 part a Only handwritten solution accepted 3.19 Nonnegative weighted sums and integrals.(a) Show that f(x)ar > 0, and |2] denotes the ith largest component of x. (You can use the fact thatf (x) = E, x1a] is convex on R".)2- aixji] is a convex function of x, where a1 > a2 > ·..>(b) Let T(x,w) denote the trigonometric polynomialT(x,w) = x1 + x2 cos w + x3 cos 2w + ... + xn cos(n – 1)w.Show that the functionc2nf(x) = - | log T(x,w) dwis convex on {x € R" | T(x,w) > 0, 0

Convexity is a significant property of a real-valued function. Suppose two points are taken on the…

Answered: 3.19 Nonnegative weighted sums and…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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3.19 Nonnegative weighted sums and integrals. (a) Show that f(x) = L;-1 aixji] is a convex function of x, where ai 2 a2 > ·> ar > 0, and æi] denotes the ith largest component of x. (You can use the fact that f(x) = E-1 "[ is convex on R".) (b) Let T(x,w) denote the trigonometric polynomial