2n+1 In Section 8, Example 2, if you follow the same procedure for the result is Зп-5 N = + ??? 9e 3 What integer should replace ????
2n+1 In Section 8, Example 2, if you follow the same procedure for the result is Зп-5 N = + ??? 9e 3 What integer should replace ????
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
What number is ???

Transcribed Image Text:2n+1
In Section 8, Example 2, if you follow the same procedure for
the result is
3n-5'
???
N
9€
What integer should replace ????

Transcribed Image Text:Prove lim n+ = .
Example 2
Зп+1
7n-4
40 2. Sequences
Discussion. For each e > 0, we need to to decide how big n must
be to guarantee n - 2< e. Thus we want
7n-4
21n + 7 – 21n + 12
7(4n – 4)
19
< E.
7(7n – 4)
or
Since 7n – 4 > 0, we can drop the absolute value and manipulate
the inequality further to "solve" for n:
19
< 7n – 4
7€
19
+ 4 < 7n
7€
4
< n.
19
or
or
49€
Our steps are reversible, so we will put N =
could have chosen N to be any number larger than
19
49€
+. Incidentally, we
19
49€
Formal Proof
19
Let e > 0 and let N
+. Then n > N implies n >
49€
19
49€
19
7e
19
hence
7e )
19
hence 7n
+ 4, hence 7n – 4 >
< €, and hence
|
7(7n-4)
Зп+1
7n-4
- < €. This proves lim
Зп+1
7n-4
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

