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Question 1 Which of the following statements (for one dimensional systems) is/are true (if any)? 1. There exists a smooth function f(x), such that i = f(x) has every real number as a fixed point. 2. There exists a smooth function f(x), such that i = f(x) has a fixed point at every integer, and only at integer numbers. 3. There exists a smooth function f(x), such that i = f(x) has precisely three stable fixed points.

Question 1 Which of the following statements (for one dimensional systems) is/are true (if any)? 1. There exists a smooth function f(x), such that i = f(x) has every real number as a fixed point. 2. There exists a smooth function f(x), such that i = f(x) has a fixed point at every integer, and only at integer numbers. 3. There exists a smooth function f(x), such that i = f(x) has precisely three stable fixed points.

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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Question 1 Which of the following statements (for one dimensional systems) is/are true (if any)? 1. There exists a smooth function f(x), such that i = f(x) has every real number as a fixed point. 2. There exists a smooth function f(x), such that i = f(x) has a fixed point at every integer, and only at integer numbers. 3. There exists a smooth function f(x), such that i = f(x) has precisely three stable fixed points. 4. There exists a smooth function f(x), such that i = f(x) has no fixed points. 5. There exists a smooth function f(x), such that i = f(x) has precisely 100 fixed points.
Transcribed Image Text:Question 1 Which of the following statements (for one dimensional systems) is/are true (if any)? 1. There exists a smooth function f(x), such that i = f(x) has every real number as a fixed point. 2. There exists a smooth function f(x), such that i = f(x) has a fixed point at every integer, and only at integer numbers. 3. There exists a smooth function f(x), such that i = f(x) has precisely three stable fixed points. 4. There exists a smooth function f(x), such that i = f(x) has no fixed points. 5. There exists a smooth function f(x), such that i = f(x) has precisely 100 fixed points.
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