2. Let f : (0, –→R such that f(x) = x². Show that f(x) < r. • Show that f has no fixed point on (0, ]. Hint: Assume there were f(c) = c and derive a contradiction.
2. Let f : (0, –→R such that f(x) = x². Show that f(x) < r. • Show that f has no fixed point on (0, ]. Hint: Assume there were f(c) = c and derive a contradiction.
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
Please see attached. Thanks. 10.2.b. (Second bullit point).
![2. Let f : (0, ] → R such that f(x) = z².
• Show that f(x) < x.
• Show that f has no fixed point on (0, 1. Hint: Assume there were f(c) = c and derive
a contradiction.
• Show that the function f(x) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set
f(x) = z and show the resulting equation has a solution in [0. o0) using the the IVP.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F4575e423-178c-4a34-b93e-7659b5154d87%2F8udl0i_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let f : (0, ] → R such that f(x) = z².
• Show that f(x) < x.
• Show that f has no fixed point on (0, 1. Hint: Assume there were f(c) = c and derive
a contradiction.
• Show that the function f(x) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set
f(x) = z and show the resulting equation has a solution in [0. o0) using the the IVP.
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