Question 6 Consider a function f R R Denote by f the n fold

Last updated: 1/2/2023

Question 6 Consider a function f R R Denote by f the n fold composition of f with itself f n fofo of n times In the examples below we will use the n fold composition for two real valued functions f and g A Let f x x Define the following sequence an n 0 1 if n 0 B Let g x 3 847 1 r Define the following sequence b 0 5 g 0 5 if n 0 if n 0 For each of the sequences describe their behavior as n their asymptotic behavior is there a limit for the sequence itself or are there limits for any subsequence s of it You may need computer simulation to find out this behavior Your answer for both A and B should describe the asymptotic behavior in English and also its formalization using predicates and quantifiers the quantifiers can be over either domain N or R If necessary you can introduce constants to denote the limits in your predicate formulas