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In this question we prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set. For example, if the points are (1,2) and (3, 4), enter in the format (1,2),(3,4) (a) R – {(r,9) : =²? + 3? > 1, y < 0} (-1,-1).(-1,1) (») S – {(z,9) : ( – 3)2 + y? < 13}u{(z,9) : ( + 1)² + 3² < 5} = {(z,9):=² > 2}n{z.») : =² <3}

In this question we prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set. For example, if the points are (1,2) and (3, 4), enter in the format (1,2),(3,4) (a) R – {(r,9) : =²? + 3? > 1, y < 0} (-1,-1).(-1,1) (») S – {(z,9) : ( – 3)2 + y? < 13}u{(z,9) : ( + 1)² + 3² < 5} = {(z,9):=² > 2}n{z.») : =² <3}

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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In this question we prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set. For example, if the points are (1,2) and (3,4), enter in the format (1,2),(3,4) (2) R – {(r,9) : =? + y? > 1, y < 0} (-1,-1).(-1,1) {(1,9) : (2 – 3)² + 3² s 13}u{(=,y) : (z +1)² + y? < 5} (0)T = {(z,v) : =? > 2}n {(z,9) : y² < 5}
Transcribed Image Text:In this question we prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set. For example, if the points are (1,2) and (3,4), enter in the format (1,2),(3,4) (2) R – {(r,9) : =? + y? > 1, y < 0} (-1,-1).(-1,1) {(1,9) : (2 – 3)² + 3² s 13}u{(=,y) : (z +1)² + y? < 5} (0)T = {(z,v) : =? > 2}n {(z,9) : y² < 5}
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