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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.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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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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