6. Analyze whether the following sets are convex: Please make the answers step by step as explicit as possible. thank you a) A = {(x, y) ∈ R2 : y ≥ x2}b) B = {x, y) ∈ R2 : y ≥ |x|}c) C = {x, y) ∈ R2 : x2 + 3y2 ≤ xy + 5}d) D = {(x, y, z) ∈ R3 : x + y = 2; z = 5}e) A ∩ Bf ) C1 = {(x, y, z) ∈ R3 : 2x − 5 + z ≤ 5, x < 16}.g) C2={(x,y,z,w)∈R4:x−3y=x+2w}.h) C3={(x,y)∈R2:x2+y2≤16}.i ) C4={(x,y)∈R2:2xy−x2−y2≥4}.

6. Analyze whether the following sets are convex: Please make the answers step by step as explicit as possible. thank you a) A = {(x, y) ∈ R2 : y ≥ x2}b) B = {x, y) ∈ R2 : y ≥ |x|}c) C = {x, y) ∈ R2 : x2 + 3y2 ≤ xy + 5}d) D = {(x, y, z) ∈ R3 : x + y = 2; z = 5}e) A ∩ Bf ) C1 = {(x, y, z) ∈ R3 : 2x − 5 + z ≤ 5, x < 16}.g) C2={(x,y,z,w)∈R4:x−3y=x+2w}.h) C3={(x,y)∈R2:x2+y2≤16}.i ) C4={(x,y)∈R2:2xy−x2−y2≥4}.

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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