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2. (i) On R², consider the metric d(x, y) = 2x1-9₁ +4₂-9₂- In this metric, sketch the closed ball B₁ (0) of radius 1 centred at the origin. Explain briefly how you produced the sketch. Vee - (ii) Find two points y, z € R² such that y, z € B₁(0) and d(y, z) = 2, where d is the metric in Q2(i).

2. (i) On R², consider the metric d(x, y) = 2x1-9₁ +4₂-9₂- In this metric, sketch the closed ball B₁ (0) of radius 1 centred at the origin. Explain briefly how you produced the sketch. Vee - (ii) Find two points y, z € R² such that y, z € B₁(0) and d(y, z) = 2, where d is the metric in Q2(i).

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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2. (i) On R², consider the metric d(x, y) = 2x1-9₁ +42-9₂- In this metric, sketch the closed ball B₁ (0) of radius 1 centred at the origin. Explain briefly how you produced the sketch. Vee - (ii) Find two points y, z € R2 such that y, z € B₁(0) and d(y, z) = 2, where d is the metric in Q2(i). Da
Transcribed Image Text:2. (i) On R², consider the metric d(x, y) = 2x1-9₁ +42-9₂- In this metric, sketch the closed ball B₁ (0) of radius 1 centred at the origin. Explain briefly how you produced the sketch. Vee - (ii) Find two points y, z € R2 such that y, z € B₁(0) and d(y, z) = 2, where d is the metric in Q2(i). Da
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