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• Show that f(x) < x. • Show that ƒ has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = z from [0, ∞) to [0, ∞0) has a fixed point c. Hint: Set f (x) = x and show the resulting equation has a solution in [0, 0) using the the IVP. 1+x²

• Show that f(x) < x. • Show that ƒ has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. • Show that the function f(x) = z from [0, ∞) to [0, ∞0) has a fixed point c. Hint: Set f (x) = x and show the resulting equation has a solution in [0, 0) using the the IVP. 1+x²

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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=. Let f : (0, → R such that f(x) = x². • Show that f(x) < x. • Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. 1 • Show that the function f(x) = from [0, 0) to [0, 0) has a fixed point c. Hint: Set f (x) = x and show the resulting equation has a solution in [0, ∞) using the the IVP. 1+x²
Transcribed Image Text:=. Let f : (0, → R such that f(x) = x². • Show that f(x) < x. • Show that f has no fixed point on (0, 3]. Hint: Assume there were f(c) = c and derive a contradiction. 1 • Show that the function f(x) = from [0, 0) to [0, 0) has a fixed point c. Hint: Set f (x) = x and show the resulting equation has a solution in [0, ∞) using the the IVP. 1+x²
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