HW Prove: If limint x=L then I subsey →L
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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this is my homework, and not graded at all
Prove this theorem, by writing in two columns
•statements •justifications
please must follow the theorem format
![Please solve my homework
question like this (statement
and justifications) columns
1) Given any ɛ > 0, choose N, = = +1
1) OK because ɛ > 0
%3D
2) For any n > N, we have <n
2) by a+1 > a
3) 8 – E < En
3) no switch when mult by ɛ > 0
4) 8 < en + ɛ
4) adding ɛ to both sides
5) 8 < e(n+ 1)
5) algebra (factoring)
6) <E
6) no switch when mult by 1/(n+1) > 0 because n+1 > 0.
n+1
7) E
7) defn of abs value
8) - < e
Sn+8
8) algebra
n+1
n+1
9) - <
8(n+1)
n+1
8n
9) algebra
n+1
- 8| < e.
10) algebra
QED
n+1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c2e24fa-e538-45c5-912e-7c4fdc15070f%2F3aa64287-5293-40e9-baf0-1351d6d6450c%2Fb14itep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please solve my homework
question like this (statement
and justifications) columns
1) Given any ɛ > 0, choose N, = = +1
1) OK because ɛ > 0
%3D
2) For any n > N, we have <n
2) by a+1 > a
3) 8 – E < En
3) no switch when mult by ɛ > 0
4) 8 < en + ɛ
4) adding ɛ to both sides
5) 8 < e(n+ 1)
5) algebra (factoring)
6) <E
6) no switch when mult by 1/(n+1) > 0 because n+1 > 0.
n+1
7) E
7) defn of abs value
8) - < e
Sn+8
8) algebra
n+1
n+1
9) - <
8(n+1)
n+1
8n
9) algebra
n+1
- 8| < e.
10) algebra
QED
n+1
![HW Prove: If limint x=L
then I subsey X,>h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c2e24fa-e538-45c5-912e-7c4fdc15070f%2F3aa64287-5293-40e9-baf0-1351d6d6450c%2F7nk9e2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:HW Prove: If limint x=L
then I subsey X,>h
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