sinh xn • Int1 • In+1 = Xn 3.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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part d & e only

Exercise 1.
Calculator Experiment) Use a calculator to explore the behavior of
the following maps:
• Cn+1
• In+1= exp In
• In+1 = cot xn
• Int1 i
sinh In
3.
• Xn+1 = Xn
= In
• In+1 = ln xn
• In+1 = tan xn
• In+1 = tanh xn
Choose an appropriate initial xo and repeatedly press the corresponding function key on you
calculator. What do you observe? Try a few (three or four) numbers sufficiently spaced
in the function domain. Do you obtain different behaviors based on the initial number
chosen? Explain your observation mathematically using the techniques explained in our
lectures (fixed points, linear stability, cobwebs, etc.).
Transcribed Image Text:Exercise 1. Calculator Experiment) Use a calculator to explore the behavior of the following maps: • Cn+1 • In+1= exp In • In+1 = cot xn • Int1 i sinh In 3. • Xn+1 = Xn = In • In+1 = ln xn • In+1 = tan xn • In+1 = tanh xn Choose an appropriate initial xo and repeatedly press the corresponding function key on you calculator. What do you observe? Try a few (three or four) numbers sufficiently spaced in the function domain. Do you obtain different behaviors based on the initial number chosen? Explain your observation mathematically using the techniques explained in our lectures (fixed points, linear stability, cobwebs, etc.).
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