3. Let== |arctan(x) — arctan(y)|d₂(x, y):for x, y = R.(a) Show that d₂ is a metric on R.(b) Are de and d₂ equivalent?

Answered: Image /qna-images/answer/73857145-761b-451e-9eba-355a0bb21a5b.jpg

Answered: 3. Let d₂(x, y) = |arctan(x) —…

3. Let d₂(x, y) = |arctan(x) — arctan(y)| for x, y € R. (a) Show that d₂ is a metric on R. (b) Are de and d₂ equivalent?

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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Question

3. Let
=
= |arctan(x) — arctan(y)|
d₂(x, y):
for x, y = R.
(a) Show that d₂ is a metric on R.
(b) Are de and d₂ equivalent?

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