Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
MAΤΗ Μ413 DANIELE ROSSO HW 12 (1) Prove that the function f(r) = is not uniformly contimuous on (0, 1). (Hint: find two sequences (r,}nEN and {žn}n€N such that |r,n – žn| < but |f(xn) – f(2n)| 2 1 for all n.) (2) Prove that the function f(r) = VT is uniformly continuous on [-1, ). (Hint: follow the example of f(r) = V from class, but considering the sets (-1, 1] and (1/2, ox)) (3) Prove that the piece-wise function defined by 3r if r < -2 f(z) = {-4 if a = -2

MAΤΗ Μ413 DANIELE ROSSO HW 12 (1) Prove that the function f(r) = is not uniformly contimuous on (0, 1). (Hint: find two sequences (r,}nEN and {žn}n€N such that |r,n – žn| < but |f(xn) – f(2n)| 2 1 for all n.) (2) Prove that the function f(r) = VT is uniformly continuous on [-1, ). (Hint: follow the example of f(r) = V from class, but considering the sets (-1, 1] and (1/2, ox)) (3) Prove that the piece-wise function defined by 3r if r < -2 f(z) = {-4 if a = -2

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 need help with number 2

11:54 1 < Ваck hw12-M413.pdf Q МАТH M413 DANIELE ROSSO HW 12 (1) Prove that the function f(r) = is not uniformly continuous on (0, 1]. (Hint: find two sequences (a,}nEN and {2,}nEN such that ,- zn| < 1 but |f(x,) – f (2,)| 21 for all n.) (2) Prove that the function f(x) = VE is uniformly continuous on [-1, o0). (Hint: follow the example of f(r) = Va from class, but considering the sets [-1, 1] and [1/2, ) ) (3) Prove that the piece-wise function defined by 1 3z - if r < -2 f(1) = {-4 if r = -2 |1² + 5x + } if a > -2 is integrable on [-4,7). (Hint: do not use upper and lower sums, use a theorem) 000 o00 Dashboard Calendar To Do Notifications Inbox
Transcribed Image Text:11:54 1 < Ваck hw12-M413.pdf Q МАТH M413 DANIELE ROSSO HW 12 (1) Prove that the function f(r) = is not uniformly continuous on (0, 1]. (Hint: find two sequences (a,}nEN and {2,}nEN such that ,- zn| < 1 but |f(x,) – f (2,)| 21 for all n.) (2) Prove that the function f(x) = VE is uniformly continuous on [-1, o0). (Hint: follow the example of f(r) = Va from class, but considering the sets [-1, 1] and [1/2, ) ) (3) Prove that the piece-wise function defined by 1 3z - if r < -2 f(1) = {-4 if r = -2 |1² + 5x + } if a > -2 is integrable on [-4,7). (Hint: do not use upper and lower sums, use a theorem) 000 o00 Dashboard Calendar To Do Notifications Inbox
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
Similar questions
  • SEE MORE 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