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Multivariable Limit

  • Thread starter karens
  • Start date
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1. Homework Statement
Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|].
Using this, prove: lim(x,y)→(0,0) f(x, y) = 0


2. Homework 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.
 
307
3
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).
 

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