Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 2.2, Problem 10E
Interpretation Introduction
Interpretation:
To find the equation for the function
Concept Introduction:
➢ Fixed points are the points where the function
➢ Using this property of the fixed point, the equation for the stated property can be found.
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Students have asked these similar questions
2. Let a, b be real numbers for which b > a. Let functions f, g, h be defined on a domain [a, b] in the following manner.
when x = a;
a+b
2
when x = a;
f(x) =
g(x) =
h(x) = (x – a)(x – b).
when x > a.
when x > a.
x-a
(a) Sketch a graph of functions f, g, h.
(b) Function h is continuous at every point in its domain, but functions f, g are not continuous at x = a. Explain.
(c) Function ƒ does not have a maximum value. Explain.
(d) Function
does not have a minimum value. Explain.
(e) Function h attains both a maximum value and a minimum value. The maximum value occurs at the points x = a
and x = b; and the minimum value occurs at the point x =
a+b
말. Explain.
For each point on the graph of y=f(x), is a corresponding point on the graph of y=√ √ f(x) exists,
determine it.
(3,-4)
a. (3,2)
b. (3,-2)
c. (3,√2)
d. Does not exist
Let us define a number a to be a fixed point of a function f if a = f(a). (For example, if
f (x) = -x², then x =
-1 is a fixed point because f(–1) = -1.)
Prove that if f'(x) # 1 for all numbers x, then f has at most one fixed point.
Chapter 2 Solutions
Nonlinear Dynamics and Chaos
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5E
Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.7 - Prob. 1ECh. 2.7 - Prob. 2ECh. 2.7 - Prob. 3ECh. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9E
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