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(a) Use the definition of continuity to show that the function Jx, if æ is rational 10, D(æ) = if x is irrational is continuous at 0. (b) Let a + 0. Use the definition of continuity to show that D is not continuous at a.

(a) Use the definition of continuity to show that the function Jx, if æ is rational 10, D(æ) = if x is irrational is continuous at 0. (b) Let a + 0. Use the definition of continuity to show that D is not continuous at a.

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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12:18 Problem 9.1.20. (a) Use the definition of continuity to show that the function Sx, D(x) 10, if x is rational if x is irrational is continuous at 0. (b) Let a + 0. Use the definition of continuity to show that D is not continuous at a. Hint. You might want to break this up into two cases where a is rational or irrational. Show that no choice of 8 > 0 will work for ɛ = | a|. Note that Theorem 3.0.11 of Chapter 3 will probably help here. Theorem 3.0.11. a. Between any two distinct real numbers there is a rational number. b. Between any two distinct real numbers there is an irrational number. in-context II II
Transcribed Image Text:12:18 Problem 9.1.20. (a) Use the definition of continuity to show that the function Sx, D(x) 10, if x is rational if x is irrational is continuous at 0. (b) Let a + 0. Use the definition of continuity to show that D is not continuous at a. Hint. You might want to break this up into two cases where a is rational or irrational. Show that no choice of 8 > 0 will work for ɛ = | a|. Note that Theorem 3.0.11 of Chapter 3 will probably help here. Theorem 3.0.11. a. Between any two distinct real numbers there is a rational number. b. Between any two distinct real numbers there is an irrational number. in-context II II
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