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Let O = (0,0), and a = (2, –1) be points in R2. Set G = B (O, 1) = {v = (x, y) € R² : d2(O, v) < 1} H = Bª (a, 1) = {v = (r, y) € R²: d1(a, v) < 1} %3D (a) Describe G and H in terms of (x, y)-curves alone, and where applicable without making use of any absolute value symbol. (b) Give the set S of all possible values of y if v = (y) E H. (c) Sketch G and H in separate Cartesian coordinates systems (r, y), indicating only O, a and all possible r-intercepts and y-intercepts.

Let O = (0,0), and a = (2, –1) be points in R2. Set G = B (O, 1) = {v = (x, y) € R² : d2(O, v) < 1} H = Bª (a, 1) = {v = (r, y) € R²: d1(a, v) < 1} %3D (a) Describe G and H in terms of (x, y)-curves alone, and where applicable without making use of any absolute value symbol. (b) Give the set S of all possible values of y if v = (y) E H. (c) Sketch G and H in separate Cartesian coordinates systems (r, y), indicating only O, a and all possible r-intercepts and y-intercepts.

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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(2, –1) be points in R?. Set G = Bdª(O, 1) = {v = (r, y) E R²: dz(O, v) < 1} H = Bª (a, 1) = {v = (x, y) E R²: d1(a, v) < 1} Let O = (0,0), and a = (a) Describe G and H in terms of (x, y)-curves alone, and where applicable without making use of any absolute value symbol. (b) Give the set S of all possible values of y if v = (, y) e H. (c) Sketch G and H in separate Cartesian coordinates systems (r, y), indicating only 0,a and all possible r-intercepts and y-intercepts.
Transcribed Image Text:(2, –1) be points in R?. Set G = Bdª(O, 1) = {v = (r, y) E R²: dz(O, v) < 1} H = Bª (a, 1) = {v = (x, y) E R²: d1(a, v) < 1} Let O = (0,0), and a = (a) Describe G and H in terms of (x, y)-curves alone, and where applicable without making use of any absolute value symbol. (b) Give the set S of all possible values of y if v = (, y) e H. (c) Sketch G and H in separate Cartesian coordinates systems (r, y), indicating only 0,a and all possible r-intercepts and y-intercepts.
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