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3. We study the function f defined below: 9-11 r is rational - if x is irrational Prove that f is nowhere continuous except at x = 0. That is, you need to prove the following two statements. f is continuous at x = 0. f is not continuous at a = a for any a # 0.

3. We study the function f defined below: 9-11 r is rational - if x is irrational Prove that f is nowhere continuous except at x = 0. That is, you need to prove the following two statements. f is continuous at x = 0. f is not continuous at a = a for any a # 0.

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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3. We study the function f defined below: if r is rational if r is irrational -x-4 Prove that f is nowhere continuous except at x = 0. That is, you need to prove the following two statements. f is continuous at x = 0. f is not continuous at r = a for any a = 0.
Transcribed Image Text:3. We study the function f defined below: if r is rational if r is irrational -x-4 Prove that f is nowhere continuous except at x = 0. That is, you need to prove the following two statements. f is continuous at x = 0. f is not continuous at r = a for any a = 0.
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