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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

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

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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Q9 For each nonzero rational number in the interval (0, 1), write x as p/q where p, q are integers with no common factors and p, q> 0, and then define f(x) = 1. Also define f(x) = 0 for all æ € (0, 1) \ Q. Show ƒ is continuous at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) nQ.
Transcribed Image Text:Q9 For each nonzero rational number in the interval (0, 1), write x as p/q where p, q are integers with no common factors and p, q> 0, and then define f(x) = 1. Also define f(x) = 0 for all æ € (0, 1) \ Q. Show ƒ is continuous at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) nQ.
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