• In+1 = tan xn = tan • In+1 = tanh xm

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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only parts G & F, please!!!!

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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