Let f:(1,3)→ R be continuous on (1, 3). Then, for each & >0 and each u € (1,3) there exists a 5(e,u) >0 such that |f(x)-f(u)| <ɛ whenever |x-u|

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
icon
Concept explainers
Topic Video
Question
Don't write the details, just give me the final answer quickly please
Let f:(1,3) → R be continuous on (1, 3). Then, for each ɛ >0 and each u € (1,3)
there exists a 0(E,u) >0 such that |f(x)-f(u)| <ɛ whenever |x-u|<o(e,u). Let
A= {0(E,u): ɛ E (0, ), u € (1,3)}. Which of the following sets A would guarantee
that f is uniformly continuous on (1,3)?
Select one:
O a. none of the listed sets guarantees the uniform continuity of f over (1,3).
O b. A = {T
|In(3-u)|
ɛ E (0, 00), u E (1,3)}
O c. A = {E(3-u): ɛ E (0,00), u € (1,3)}
O d. A = { EE (0, 0), u € (1,3)}
Transcribed Image Text:Let f:(1,3) → R be continuous on (1, 3). Then, for each ɛ >0 and each u € (1,3) there exists a 0(E,u) >0 such that |f(x)-f(u)| <ɛ whenever |x-u|<o(e,u). Let A= {0(E,u): ɛ E (0, ), u € (1,3)}. Which of the following sets A would guarantee that f is uniformly continuous on (1,3)? Select one: O a. none of the listed sets guarantees the uniform continuity of f over (1,3). O b. A = {T |In(3-u)| ɛ E (0, 00), u E (1,3)} O c. A = {E(3-u): ɛ E (0,00), u € (1,3)} O d. A = { EE (0, 0), u € (1,3)}
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Application of Algebra
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,