Is f continuous at (0,0) and how to show it with curves?

[juanandresrua]

Homework Statement

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?

Homework Equations

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.

 

[SammyS]

Homework Statement

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?

Homework Equations

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.

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: $$ \frac{x^2+y^2}{x-y}=2\ \ .$$

 

[HallsofIvy]

The line x= y is certainly important!

 

[juanandresrua]

I just did it. Thanks to both.