1. What are the eventually fixed points for A(x) = [x? 2. Let F(x) = 1-x. Show that 0 lies on a 2-cycle for this function. 3. Consider the function F(x) = /x-2/. a. What are the fixed points for F? b. If m is an odd integer, what can you say about the orbit of m? c. What happens to the orbit if m is even? 4. How many fixed points does the function T(x) = tan(x) have? 5. Does the function F(x) =-x have a cycle of prime period 2? 6. For which values of o and b does the linear function L(x) = ax +b have a cycle of prime period 2? 7. let T(x) be Tent Map then find (a)Find a formula for T(x). (b). Sketch the graphs of T and T. (c) Find all fixed points for Tand T. (d). Find an explicit formula for T(x) and sketch the graph of T. (f). What does the graph of T look like?
1. What are the eventually fixed points for A(x) = [x? 2. Let F(x) = 1-x. Show that 0 lies on a 2-cycle for this function. 3. Consider the function F(x) = /x-2/. a. What are the fixed points for F? b. If m is an odd integer, what can you say about the orbit of m? c. What happens to the orbit if m is even? 4. How many fixed points does the function T(x) = tan(x) have? 5. Does the function F(x) =-x have a cycle of prime period 2? 6. For which values of o and b does the linear function L(x) = ax +b have a cycle of prime period 2? 7. let T(x) be Tent Map then find (a)Find a formula for T(x). (b). Sketch the graphs of T and T. (c) Find all fixed points for Tand T. (d). Find an explicit formula for T(x) and sketch the graph of T. (f). What does the graph of T look like?
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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Transcribed Image Text:1. What are the eventually fixed points for A(x) = [x?
2. Let F(x) = 1-x. Show that 0 lies on a 2-cycle for this function.
3. Consider the function F(x) = /x-2/.
a. What are the fixed points for F?
b. If m is an odd integer, what can you say about the orbit of m?
c. What happens to the orbit if m is even?
4. How many fixed points does the function T(x) = tan(x) have?
5. Does the function F(x) = -x have a cycle of prime period 2?
6. For which values of o and b does the linear function L(x) = ax + b have
a cycle of prime period 2?
7. let T(x) be Tent Map then find
(a)Find a formula for T(x).
(b). Sketch the graphs of T and T.
(c) Find all fixed points for Tand T.
(d). Find an explicit formula for T(x) and sketch the graph of T.
(f). What does the graph of T look like?
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