Theorem 8. i) Every solution of Eq.(2) is bounded from above such that xo #0, x-1#0 and a > 0 min(,) such that xo # 0 , x-1 # ii)Every solution of Eq.(2) is bounded from down by M = 0 and a <0. Proof: i) Let {an}n=-k 00 be a solution of Eq.(2). It follows from Eq.(2) that Xn 1 Xn+1 = x + a Then 1 Xn S for all n 2 0. Xn-1 This means that every solution of eq(2) is bouneded from above by M = max(, ) such that xo + 0, x-1 # 0 and a > 0. ii) Easy to prove as in i).
Theorem 8. i) Every solution of Eq.(2) is bounded from above such that xo #0, x-1#0 and a > 0 min(,) such that xo # 0 , x-1 # ii)Every solution of Eq.(2) is bounded from down by M = 0 and a <0. Proof: i) Let {an}n=-k 00 be a solution of Eq.(2). It follows from Eq.(2) that Xn 1 Xn+1 = x + a Then 1 Xn S for all n 2 0. Xn-1 This means that every solution of eq(2) is bouneded from above by M = max(, ) such that xo + 0, x-1 # 0 and a > 0. ii) Easy to prove as in i).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show me the steps of determine blue and inf is here
Transcribed Image Text:Xn
Xn+1
(xn) + a
where (xo) + -a
In order to do this we introduce the following notations:
Let xo = a
Consider the following notations:
Transcribed Image Text:Theorem 8. i) Every solution of Eq.(2) is bounded from above such that xo + 0, x-1 #0 and a > 0
ii)Every solution of Eq. (2) is bounded from down by M = min(,,) such that xo + 0, x-1#
0 аnd a < 0.
Proof:
i) Let {xn} k be a solution of Eq.(2). It follows from Eq.(2) that
n=-k
Xn
1
Xn+1
xn + a
Then
1
for all
n > 0.
Xn-1
This means that every solution of eq(2) is bouneded from above by M = max(, ) such that
xo + 0, x-1 70 and a > 0 .
ii) Easy to prove as in i) .
Expert Solution
Step 1
Given : Equation (2)
where .
To prove : Theorem 8, part (i)
Step by step
Solved in 2 steps
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