Does there exist a function u : R² → R that is not continuous at 0 E R², but whose restriction to every polynomial curve going through 0 e R? is continuous? By a poly- nomial curve we mean the parameterized curve (t, p(t)) where p is some polynomial, or a rotated version of (t, p(t)).

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%

Pls kindly help to use Analysis to proof it. thanks

Does there exist a function u : R? → R that is not continuous at 0 E R², but whose
restriction to every polynomial curve going through 0 e R? is continuous? By a poly-
nomial curve we mean the parameterized curve (t, p(t)) where p is some polynomial, or
a rotated version of (t, p(t)).
Transcribed Image Text:Does there exist a function u : R? → R that is not continuous at 0 E R², but whose restriction to every polynomial curve going through 0 e R? is continuous? By a poly- nomial curve we mean the parameterized curve (t, p(t)) where p is some polynomial, or a rotated version of (t, p(t)).
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
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,