# Multivariable Continuity

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1. Feb 18, 2015

### juanandresrua

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. Feb 18, 2015

### SammyS

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

3. Feb 19, 2015

### HallsofIvy

The line x= y is certainly important!

4. Feb 20, 2015

### juanandresrua

I just did it. Thanks to both.