Q9For each nonzero rational number in the interval (0, 1), write x as p/q where p, q are integers with no commonfactors and p, q> 0, and then define f(x) = 1. Also define f(x) = 0 for all æ € (0, 1) \ Q. Show ƒ is continuousat each point of (0, 1) \ Q and discontinuous at each point of (0, 1) nQ.

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Answered: For each nonzero rational number in the…

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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For each nonzero rational number in the interval (0, 1), write a as p/q where p, q are integers with no common factors and p, q> 0, and then define f(x) = . Also define f(x) = 0 for all x = (0, 1) \ Q. Show f is continuous at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) Q