Let f: (0, 1)→ R be bounded but such that lim f does not exist. Show that there are two sequences (x₂) and (v.) in (0, 1) with lim(x) = 0 - lim(y) but such that (f(x)) and (f(x)) x-0

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
Question
Let \( f : (0, 1) \to \mathbb{R} \) be bounded but such that \( \lim_{x \to 0} f \) does not exist. Show that there are two sequences \( (x_n) \) and \( (y_n) \) in \( (0, 1) \) with \( \lim(x_n) = 0 = \lim(y_n) \), but such that \( (f(x_n)) \) and \( (f(y_n)) \) exist but are not equal.
Transcribed Image Text:Let \( f : (0, 1) \to \mathbb{R} \) be bounded but such that \( \lim_{x \to 0} f \) does not exist. Show that there are two sequences \( (x_n) \) and \( (y_n) \) in \( (0, 1) \) with \( \lim(x_n) = 0 = \lim(y_n) \), but such that \( (f(x_n)) \) and \( (f(y_n)) \) exist but are not equal.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
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,