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

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Homework Help Overview

The discussion revolves around the continuity of a function at the point (0,0) and the identification of the maximum region where the function is continuous. Participants are analyzing a graph to determine the behavior of the function near this point.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to understand the continuity of the function by examining curves and their relation to the graph. There is a focus on identifying specific curves that demonstrate discontinuity, with one participant suggesting the use of a constant value to explore the function further.

Discussion Status

The discussion is active, with participants sharing their thoughts and approaches. One participant has indicated they have made progress in their exploration, suggesting that some productive direction has been achieved.

Contextual Notes

There is a reference to a graph that is central to the discussion, but the specific details of the function and its properties are not fully articulated. Participants are also navigating language barriers, which may influence the clarity of their contributions.

juanandresrua
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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.
 
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juanandresrua said:

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: $$ \frac{x^2+y^2}{x-y}=2\ \ .$$
 
The line x= y is certainly important!
 
I just did it. Thanks to both.
 

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