2. Let (r) be the function defined by V(x) = 1. Let 1+x. In(x) Vovo...(x) n-copies Note that alternate definitions proceed by induction: Let V₁(x) In ((x)) or, equivalently, define Yn+1 = Y(Yn (x)). (x) and define n+1 a) What is the domain of Vn(x) for n = {1,2,3,4}? b) What is your guess for the domain of Vn in general? c) Calculate (x) for n € {1,2,3,4}. Arrange your calculation in a way to make it easily under- standable. There are various approaches here and some are easier to understand than others. Do not be afraid to start on one approach and give it up in favour of another. d) What is your guess for (r) in general. You are not asked to prove this by mathematical induction, but it is a good exercise to give it a try.
2. Let (r) be the function defined by V(x) = 1. Let 1+x. In(x) Vovo...(x) n-copies Note that alternate definitions proceed by induction: Let V₁(x) In ((x)) or, equivalently, define Yn+1 = Y(Yn (x)). (x) and define n+1 a) What is the domain of Vn(x) for n = {1,2,3,4}? b) What is your guess for the domain of Vn in general? c) Calculate (x) for n € {1,2,3,4}. Arrange your calculation in a way to make it easily under- standable. There are various approaches here and some are easier to understand than others. Do not be afraid to start on one approach and give it up in favour of another. d) What is your guess for (r) in general. You are not asked to prove this by mathematical induction, but it is a good exercise to give it a try.
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
Transcribed Image Text:2. Let (r) be the function defined by V(x) = 1. Let
1+x
In(x) Vovo...(x)
n-copies
Note that alternate definitions proceed by induction: Let V₁(x)
In (V(x)) or, equivalently, define ¥n+1 = (In(x)).
=
(x) and define Vn+1
a) What is the domain of Vn(x) for n = {1,2,3,4}?
b) What is your guess for the domain of Vn in general?
c) Calculate (x) for n € {1,2,3,4}. Arrange your calculation in a way to make it easily under-
standable. There are various approaches here and some are easier to understand than others.
Do not be afraid to start on one approach and give it up in favour of another.
d) What is your guess for (r) in general. You are not asked to prove this by mathematical
induction, but it is a good exercise to give it a try.
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