A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 4 years ago

I have a question about existence and uniqueness. It says that if f(x,y)=dy/dx and partialf/partialy are both continuous on the xy plane, then there is one and ony one solution etc... My question is, how can you tell if the function f and the partial derivative are continuous on the xy plane if they aren't even functions in the xy plane. They are functions in 3 space. You cannot even graph dy/dx= f(x,y). For instance, if dy/dx== 2y/x, that is not in the xy plane. That is a function of 2 variables in 3 space. I am confused?

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This statement of the theorem might be helpful to you: www.math.uiuc.edu/~tyson/existence.pdf. (For f and its partials you are considering a selection of inputs which you are interested in.) The function f which you gave is not continuous at (0, y) because it is not defined there. Since f is a rational function, it is continuous on its domain, so, for x and y any reals except x=0. For a function of 2 variables to be continuous at a point, you must have: f(a,b) exists, and \[\lim_{(x,y) \rightarrow (a,b)} f(x,y)\] exists, and \[\lim_{(x,y) \rightarrow (a,b)} f(x,y) = f(a,b)\] (This must hold as the (x,y) approaches (a,b) along any direction or path.)

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.