Consider the map ƒ : [0, 1] → [0, 1] given by x+1/2 0≤ x ≤ 1/2 2 - 2x 1/2 ≤ x ≤ 1 f(x) = { (a) Show that it is continuous. (b) Show that it has a cycle of length 3. (c) Find all its cycles of lengths 1, 2, 3, and 4.
Consider the map ƒ : [0, 1] → [0, 1] given by x+1/2 0≤ x ≤ 1/2 2 - 2x 1/2 ≤ x ≤ 1 f(x) = { (a) Show that it is continuous. (b) Show that it has a cycle of length 3. (c) Find all its cycles of lengths 1, 2, 3, and 4.
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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Answer b and c
![Consider the map ƒ : [0, 1] → [0, 1] given by
x+1/2
2 - 2x
f(x) = {
0≤ x ≤ 1/2
1/2 ≤ x ≤ 1
(a) Show that it is continuous.
(b) Show that it has a cycle of length 3.
(c) Find all its cycles of lengths 1, 2, 3, and 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c7b70cb-3d97-48fb-b64b-e8283a6927c3%2F28c7656d-a72a-462f-8bda-362a410377e7%2F3cevie_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the map ƒ : [0, 1] → [0, 1] given by
x+1/2
2 - 2x
f(x) = {
0≤ x ≤ 1/2
1/2 ≤ x ≤ 1
(a) Show that it is continuous.
(b) Show that it has a cycle of length 3.
(c) Find all its cycles of lengths 1, 2, 3, and 4.
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