Find an example to show that the convexity of S is necessary in Exercise 19.Reference Exercise 19:If c e R and S is a set, define cS = {cx : x e S}. Let Sbe a convex set and suppose c > 0 and d > 0. Prove thatcS + dS = (c +d)S.

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Answered: Find an example to show that the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find an example to show that the convexity of S is necessary in Exercise 19. Reference Exercise 19: If c e R and S is a set, define cS = {cx : x e S}. Let S be a convex set and suppose c > 0 and d > 0. Prove that cS + dS = (c +d)S.