1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A limit with two variables

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data

    Let
    f(x, y) =((x^2)*y)/(x^4 + y^2) if (x, y) != (0, 0) ,
    f(x,y) = 0 if (x, y) = (0, 0) .
    a) Is f continuous at (0, 0)? Prove your statement.
    b) Show that
    -1/2 ≤ f(x, y) ≤1/2
    for all (x, y).

    I have used the two path test to show that it has not limit at 0,0 hence it is not continuous there. however, ı have no idea what I should do for the b part?Is there a algebratic way to show it or should we take differential etc.?
     
  2. jcsd
  3. Apr 10, 2007 #2
    Try solving for each inequality separately, and cross multiply to get a perfect square.
     
  4. Apr 10, 2007 #3
    Are you refering to the fx and fy (the partial derivatives of f) by saying "for each inequality"?
     
  5. Apr 10, 2007 #4
    What he means is to find necessary and sufficient conditions on x,y for each of the two inequalities

    [tex]-1 \leq \frac{2x^2y}{x^4+y^2}[/tex]

    and

    [tex]1 \geq \frac{2x^2y}{x^4+y^2}[/tex]

    (ie. rearrange them, using "reversible" steps, until you find something that will tell you for which x,y they are satisfied)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A limit with two variables
Loading...