1. Limited time only! Sign up for a free 30min personal 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!

Multivariable Limit

  1. Jun 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|].
    Using this, prove: lim(x,y)→(0,0) f(x, y) = 0

    2. Relevant equations

    Definition of a limit, etc.

    3. The attempt at a solution
    I don't know how to start... I've been trying to self-teach limits for a while and Don't know how to do it with the absolute values and two variables. Help is much needed.
  2. jcsd
  3. Jun 7, 2010 #2
    Start with the definition of a limit:

    [tex] \forall \epsilon > 0\ \ \ \exists \delta > 0[/tex] such that [tex]||f(x,y) - f(x_0,y_0)|| < \epsilon[/tex] whenever [tex] ||(x,y) - (x_0,y_0)|| < \delta[/tex].

    One way to think of it is to start by fixing epsilon and then finding what delta must be (in terms of epsilon).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook