Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    We define a function f : R^2 → R by
    f(x, y) := ( x^2)/(x^2+y^2) if (x,y) dont equal (0,0)

    And f (x,y)=0 if (x,y) = (0, 0).
    (a) Prove with the /δ definition that f is continuous at (0, 0).
    Any help i know the definition just cant do it getting confused
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by omassey)
    We define a function f : R^2 → R by
    f(x, y) := ( x^2)/(x^2+y^2) if (x,y) dont equal (0,0)

    And f (x,y)=0 if (x,y) = (0, 0).
    (a) Prove with the /δ definition that f is continuous at (0, 0).
    Any help i know the definition just cant do it getting confused
    What is the \epsilon/ \delta definition? Substitute the definitions in and see what you get.
    Online

    18
    ReputationRep:
    There must be something wrong with what you've posted - f is NOT continuous at (0, 0).
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by DFranklin)
    There must be something wrong with what you've posted - f is NOT continuous at (0, 0).
    PRSOM - in my haste, I squashed the voice of doubt which emerged when noting that y=0 gives a limit of 1…
    • Thread Starter
    Offline

    0
    ReputationRep:
    This is the question coppied and pasted is it not continous since at (0,0) f=0
    Online

    18
    ReputationRep:
    (Original post by omassey)
    This is the question coppied and pasted is it not continous since at (0,0) f=0
    It's not continuous.

    Consider the function g(x) = f(x, x).

    If f was continuous, g would be too.

    But g(x) = 1/2 when x is non-zero, while g(0) = 0.
    Offline

    17
    ReputationRep:
    (Original post by omassey)
    This is the question coppied and pasted is it not continous since at (0,0) f=0
    Are you sure that it wasn't supposed to be f(x,y) = \dfrac{x^2}{\sqrt{x^2+y^2}} away from the origin?
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by omassey)
    This is the question coppied and pasted is it not continous since at (0,0) f=0
    I don't believe it was copied and pasted, since it is phrased ungrammatically. Sorry.
    • Thread Starter
    Offline

    0
    ReputationRep:
    It was,my teacher cant speak english well.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: December 5, 2014

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.