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Problem 6. Consider the set X = {(x, y) = RxR: (y≤ x² and x > 0) or (y ≥ x² and x < 0)} U {(0,0)}. 1. Draw X in the 2D plane. 2. For a € [0, +∞o) with a > 0, we define Xa= {(x,x²-ax), x ≤ R}. (a) On the same drawing as above, represent Xo, X₁ and X₂. (b) Prove that where we recall that, by definition, X = Xa [0,+∞0) U Xa= {(x, y) = R XR: a € [0, +∞) s.t. (x,y) € X₁}. [0,+∞0)

Problem 6. Consider the set X = {(x, y) = RxR: (y≤ x² and x > 0) or (y ≥ x² and x < 0)} U {(0,0)}. 1. Draw X in the 2D plane. 2. For a € [0, +∞o) with a > 0, we define Xa= {(x,x²-ax), x ≤ R}. (a) On the same drawing as above, represent Xo, X₁ and X₂. (b) Prove that where we recall that, by definition, X = Xa [0,+∞0) U Xa= {(x, y) = R XR: a € [0, +∞) s.t. (x,y) € X₁}. [0,+∞0)

Advanced Engineering Mathematics
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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Problem 6. Consider the set X = {(x, y) ER ×R: (y≤ x² and x > 0) or (y ≥ r² and x < 0)} U {(0,0)}. 1. Draw X in the 2D plane. 2. For a € [0, +∞o) with a > 0, we define X₁ = {(x, x² — ax), x≤ R}. (a) On the same drawing as above, represent X0, X₁ and X₂. (b) Prove that where we recall that, by definition, X = U Xa [0,+∞0) U X₁ = {(x, y) = R XR : € [0, +∞) s.t. (x,y) € Xa}. [0,+∞0)
Transcribed Image Text:Problem 6. Consider the set X = {(x, y) ER ×R: (y≤ x² and x > 0) or (y ≥ r² and x < 0)} U {(0,0)}. 1. Draw X in the 2D plane. 2. For a € [0, +∞o) with a > 0, we define X₁ = {(x, x² — ax), x≤ R}. (a) On the same drawing as above, represent X0, X₁ and X₂. (b) Prove that where we recall that, by definition, X = U Xa [0,+∞0) U X₁ = {(x, y) = R XR : € [0, +∞) s.t. (x,y) € Xa}. [0,+∞0)
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