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Multivariable Continuity

  1. Feb 18, 2015 #1
    1. The problem statement, all variables and given/known data

    https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xap1/v/t1.0-9/10923273_407123639463753_2874228726948727052_n.jpg?oh=27c882da16071e65bbb420147333ec38&oe=558413E4&__gda__=1434978872_d03c8531060688181560956b68c96650

    Is f continuous at (0,0)?
    What is the "maximum" region D where f is continuous?

    2. Relevant equations


    3. The attempt at a solution
    I think, by the graph, that in (0.0) the function is not continuous. However I can't realize what curves to choose for show the discontinuity.
    I actually started around curves such that
    https://scontent-mia.xx.fbcdn.net/hphotos-xpf1/v/t1.0-9/10986437_407156659460451_678008542589932086_n.jpg?oh=7655e3989f7fcce725524cbfb67cdd60&oe=55585B76 but it was useless.
    Thanks in advance. Sorry for my English.
     
  2. jcsd
  3. Feb 18, 2015 #2

    SammyS

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    What graph are you referring to?

    Try setting your function equal to some constant value, such as 2. See what is the solution to the equation: $$ \frac{x^2+y^2}{x-y}=2\ \ .$$
     
  4. Feb 19, 2015 #3

    HallsofIvy

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    The line x= y is certainly important!
     
  5. Feb 20, 2015 #4
    I just did it. Thanks to both.
     
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