c] lim s, = 0 iff lim |s„=0 %3D %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question
100%
#3 part c
Math4303Sec4_1Homework Protected View - Saved to this PC -
O Search
gn
Layout
References
Mailings
Review
View
Help
e Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.
Enable Editing
Math 4303 Homework Section 4.1 Convergence
1. Write out the first seven terms of the sequence dn
2n +1
%3D
3n-1
2. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following:
k
a] lim
- = 0
kER
4n +1
b] lim
no n+3
= 4
6n? +3n
= 3
no 2n? -5
c] lim
sin( n)
=D0
d] lim
3. Prove or provide a counterexample for the following:
a] If (s,) converges then (s) converges.
b] If (s,) converges then (s,) converges.
c] lim s, = 0 iff lim |s„ =0
4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0
5. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim =
Show that lim y, = L
6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such that
if n> N, then s, > 0
DFocus
DELL
Transcribed Image Text:Math4303Sec4_1Homework Protected View - Saved to this PC - O Search gn Layout References Mailings Review View Help e Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. Enable Editing Math 4303 Homework Section 4.1 Convergence 1. Write out the first seven terms of the sequence dn 2n +1 %3D 3n-1 2. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following: k a] lim - = 0 kER 4n +1 b] lim no n+3 = 4 6n? +3n = 3 no 2n? -5 c] lim sin( n) =D0 d] lim 3. Prove or provide a counterexample for the following: a] If (s,) converges then (s) converges. b] If (s,) converges then (s,) converges. c] lim s, = 0 iff lim |s„ =0 4. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 0 5. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim = Show that lim y, = L 6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such that if n> N, then s, > 0 DFocus DELL
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Algebraic Operations
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.
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,