(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the set of points at which the function is continuous.

F(x,y) = R.

where R is a piecewise function of :

{

x^2*y^3 / (2x^2 + y^2) ; if(x,y) != (0,0)

1 ; if(x,y) = (0,0)

}

Obviously, the first function is not defined at point (0,0), but to find

the domain of the piecewise function, I first need to see if the

first function is at least continuous.

So here is my attempt at that :

Let A = x^2 * y^3 / (2x^2 + y^2 )

the |A| is =

x^2 * |y^3|

---------------

2x^2 + y^2

well x^2 <= 2x^2 + y^2, lets call that J

so A < J * |y^3| / (J) = |y^3| = sqrt(y^6), and we see that this function

is defined at point 0 , thus lim of A as (x,y) -->(0,0) = 0. ???

So if the above is true then the peicewise function should be

defined in region R^2???

I am not sure if this is correct. The book says that the answer is :

{ (x,y) | (x,y) != (0,0) }.

I think that means the function A is not defined at 0 thus the peicewise

function is not defined at point (0,0). What did I do wrong ?

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# Check work on 2 variable function.

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