1. Determine which of the following function define a metric on R :(i) d(a, y) = V ly| + \x|*(ii) d(x, y) = Vly3 – 2*|V x, y E RV x, y ERV x, y ER(ii) d(x, y) = |a - y|

Metric: A metric, d on X is a function defined on X × X such that for all x, y, z ∈ X, which…

Answered: 1. Determine which of the following…

1. Determine which of the following function define a metric on R : (i) d(r, y) = V ly° + |x|° (ii) d(r, y) = y3 – 2°| (ii) d(x, y) = x - y 1, y ER V a, y ER V x, y ER

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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Question

1. Determine which of the following function define a metric on R :
(i) d(a, y) = V ly| + \x|*
(ii) d(x, y) = Vly3 – 2*|
V x, y E R
V x, y ER
V x, y ER
(ii) d(x, y) = |a - y|

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