Domain of a multivariable eq'n

[sjmacewan]

Ok, i think i understand this one, but it's giving me a bit of trouble in terms of comprehension, so I thought I'd get some help on it.

I need to find and sketch the domain for:

$$f(x,y)= \frac{x^2 + y^3}{x^2 + y^2 -1}$$


The way i see it, that would only be undefined when the denominator is equal to zero. So wouldn't the domain simply be:

D={(x,y)|x^2+y^2-1 /= 0}


Right?

 

[Galileo]

That's right.

 

[TD]

Seems okay; and x²+y²-1 = 0 <=> x²+y² = 1 is exactly the unit circle in the xy-plane, so a cylinder of that circle with variable heigth z.

 

[sjmacewan]

edit:
right! i knew that, when i made the unit circle connection i forgot to take the 1 over to the other side, so it wasn't making much sense.

So the sketch would basically just include the circle, stating that THAT is the only undefined place? or would the inside of the circle be excluded from the domain as well?

 

[Galileo]

f is perfectly well defined inside the unit circle, since then x^2+y^2-1 is not equal to zero.

 

[sjmacewan]

that's what i thought, since it's $$x^2+y^2=1$$ and NOT equal to or greater than.

Anywho, thanks for the quick confirmation people!