Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Theorems on limits of sequences ove that lim ab AB. 2.8. Prove that if lim u, exists, it must be unique.As.b- -A We must show that if lim u, = l, and lim u, =,, then l =2. n00 n00 By hypothesis, given any e > 0 we can find N such that l4, – 4| N, u, - 4| N Then 3= 3 + 3>|1- "n| +|"n– /|5|7 – "n + "n – '/%=|7- | Haac i.e., |4, -4| is less than any positive e (however small) and so must be zero. Thus, l

Theorems on limits of sequences ove that lim ab AB. 2.8. Prove that if lim u, exists, it must be unique.As.b- -A We must show that if lim u, = l, and lim u, =,, then l =2. n00 n00 By hypothesis, given any e > 0 we can find N such that l4, – 4| N, u, - 4| N Then 3= 3 + 3>|1- "n| +|"n– /|5|7 – "n + "n – '/%=|7- | Haac i.e., |4, -4| is less than any positive e (however small) and so must be zero. Thus, l

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
I have to explain each step of the solved problems in the picture.
Theorems on limits of sequences prove that lim ab=AB. Prove that if lim u, exists, it must be unique. As -A 2.8. We must show that if lim u, = 1, and lim u,= 2, then l = 2. By hypothesis, given any e > 0 we can find N such that 4.-4|<e when n> N, u, -4|<e when n > N Then 14-4|=14-4, +u, -4|<4-u,+|4, – 4|<;e +e =ɛ %3D Iarger c i.e., |1, -4| is less than any positive e (however small) and so must be zero. Thus, 4 = l2.
Transcribed Image Text:Theorems on limits of sequences prove that lim ab=AB. Prove that if lim u, exists, it must be unique. As -A 2.8. We must show that if lim u, = 1, and lim u,= 2, then l = 2. By hypothesis, given any e > 0 we can find N such that 4.-4|<e when n> N, u, -4|<e when n > N Then 14-4|=14-4, +u, -4|<4-u,+|4, – 4|<;e +e =ɛ %3D Iarger c i.e., |1, -4| is less than any positive e (however small) and so must be zero. Thus, 4 = l2.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS