- #1
tnutty
- 326
- 1
Homework Statement
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, let's 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 ?