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

In summary, the conversation is about determining if a function is continuous at (0,0) and finding the maximum region where it is continuous. The attempt at a solution involves looking at the graph and setting the function equal to a constant value, such as 2. The solution to this equation reveals that the line x=y is important in determining the continuity of the function.
  • #1
juanandresrua
4
0

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.
 
Physics news on Phys.org
  • #2
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: $$ \frac{x^2+y^2}{x-y}=2\ \ .$$
 
  • #3
The line x= y is certainly important!
 
  • #4
I just did it. Thanks to both.
 

What is multivariable continuity?

Multivariable continuity is a mathematical concept that describes the behavior of a function as multiple variables change at the same time. It involves analyzing the limit of a function as all variables approach a specific point.

How is multivariable continuity different from single variable continuity?

Single variable continuity refers to the behavior of a function as a single variable changes. Multivariable continuity takes into account the behavior of a function as multiple variables change simultaneously, which can lead to more complex and interesting behavior.

What is the importance of multivariable continuity in science?

Multivariable continuity is important in many scientific fields, such as physics, economics, and engineering. It allows scientists to model and understand the behavior of complex systems with multiple variables, and make predictions about their behavior under different conditions.

How is multivariable continuity applied in real-world situations?

Multivariable continuity can be applied in various real-world situations, such as predicting the behavior of chemical reactions, analyzing the motion of objects in physics, and understanding the relationship between multiple economic variables.

What are some common techniques used to study multivariable continuity?

Some common techniques used to study multivariable continuity include partial derivatives, directional derivatives, and the use of graphs and visualizations to understand the behavior of functions in multiple dimensions.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
876
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • General Discussion
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Astronomy and Astrophysics
Replies
2
Views
2K
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • General Discussion
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
3K
Back
Top