Prove by Beta and Sigma limit definition

[kidia]

Please any help.

Use the symbols \beta and \sigma definition of limit to prove that limit (x,y)\Longrightarrow(0,0)x+y/x\x^2+y\y^2=0

 

[EnumaElish]

What is a beta and sigma limit definition? Same as the epsilon and delta definition? Here are some examples:
http://archives.math.utk.edu/visual.calculus/1/definition.6/
http://omega.albany.edu:8008/calc3/several-vars-dir/lim-epsilon-delta-m2h.html
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/preciselimdirectory/PreciseLimit.html

 

[rachmaninoff]

I think beta/sigma definitions are a 2D analogue to epsilon/deltas? I'm afraid I can't find any reference to them, you'll have to define them please.

 

[quasar987]

You want to show that for a given \beta >0, you can find a number \sigma >0 such that when the distance from the origin of the point (x,y) is smaller than \sigma, then this implies that

\frac{x+y}{x^2+y^2}&lt;\beta[/itex] <br /> <br /> So we kinda want to find a function \sigma(\beta). <br /> <br /> The statement &quot;the distance from the origin of the point (x,y) is smaller than \sigma&quot; is written mathematically as \sqrt{x^2+y^2}&amp;lt;\sigma<br /> <br /> There are many solutions but here&#039;s a hint based on one:<br /> <br /> Use the fact that x+y \leq (x^2+y^2)^2 coupled with the hypothesis \sqrt{x^2+y^2}&amp;lt;\sigma to define a function \sigma(\beta).