4. Prove that a subset of R is convex if and only if it is an interval. 5. Show that the union of two convex sets is not a convex set. 7. Given v ∈ R3 0 and ϵ > 0 then let K(v, ϵ) = {x ∈ R3 : ϵ∥v∥∥x∥ ≤ ⟨v, x⟩}. show that K(v, ϵ) is convex. 13. Consider f a convex function and S a convex set. Try that X∗ = {x∗ : f(x∗) ≤ f(x), ∀x ∈ S} It is convex. Please give the answers step by step as explicit as possible. thank you
4. Prove that a subset of R is convex if and only if it is an interval. 5. Show that the union of two convex sets is not a convex set. 7. Given v ∈ R3 0 and ϵ > 0 then let K(v, ϵ) = {x ∈ R3 : ϵ∥v∥∥x∥ ≤ ⟨v, x⟩}. show that K(v, ϵ) is convex. 13. Consider f a convex function and S a convex set. Try that X∗ = {x∗ : f(x∗) ≤ f(x), ∀x ∈ S} It is convex. Please give the answers step by step as explicit as possible. thank you
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 17E: Does the relation is a brother of have a reflexive property consider one male? A symmetric property...
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4. Prove that a subset of R is convex if and only if it is an interval.
5. Show that the union of two convex sets is not a convex set.
7. Given v ∈ R3 0 and ϵ > 0 then let K(v, ϵ) = {x ∈ R3 : ϵ∥v∥∥x∥ ≤ ⟨v, x⟩}. show that K(v, ϵ) is convex.
13. Consider f a convex function and S a convex set. Try that X∗ = {x∗ : f(x∗) ≤ f(x), ∀x ∈ S} It is convex.
Please give the answers step by step as explicit as possible. thank you
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