(8 points) For each x in [0, 1], f(x) = x, if x is rational and f(x) = 1-x, if x is irrational. a) What is f(1/2)2 b) Show that f is continuous only at ½. (Hint: Let x, be sequence in [0,1] converging to ½. Show that f(x) converges to f(1/2). If the sequence x, converges to a number other than ½, what can be said about f(x)?)
(8 points) For each x in [0, 1], f(x) = x, if x is rational and f(x) = 1-x, if x is irrational. a) What is f(1/2)2 b) Show that f is continuous only at ½. (Hint: Let x, be sequence in [0,1] converging to ½. Show that f(x) converges to f(1/2). If the sequence x, converges to a number other than ½, what can be said about f(x)?)
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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![(8 points) For each x in [0, 1], f(x) = x, if x is rational and f(x) = 1-x, if x is irrational.
(a) What is f(1/2)?
(b) Show that f is continuous only at 2. (Hint: Let x, be sequence in [0,1] converging to ½.
Show that f(x) converges to f(1/2). If the sequence x, converges to a number other than ½,
what can be said about f(x)?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e714d6-c3d6-4fe9-9c10-b4b8c64f125f%2Fa0b68a27-49b9-4c8a-961e-8e3552361a58%2F8cbnq4s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(8 points) For each x in [0, 1], f(x) = x, if x is rational and f(x) = 1-x, if x is irrational.
(a) What is f(1/2)?
(b) Show that f is continuous only at 2. (Hint: Let x, be sequence in [0,1] converging to ½.
Show that f(x) converges to f(1/2). If the sequence x, converges to a number other than ½,
what can be said about f(x)?)
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