Sketch the domain of the function f (x, y) when:

[mati89]

Sketch the domain of the function f (x, y) when:

a)
[tex]f(x,y) =\sqrt{1-xy}[/tex]*ln(xy)
b)
[tex]f(x,y)= \frac{\sqrt{xy-y^{2}}}{ln(1-x^{2}-y^{2})}[/tex]
c)
[tex]f(x,y)=xln(x-y)-\sqrt{xy}[/tex]
d)
[tex]f(x,y) =arc sin(y-2x)-\frac{x^{2}+y^{2}-16}{\sqrt{xy}}[/tex]

[Guest]

For (a), in order that ln(xy) exist, xy must be positive. In order that [tex]\sqrt{1- xy}[/tex] exist, xy must be less than or equal to 1, Both are satisfied when (x, y) lies above the positive x and y axes and below the graph if y= 1/x for x positive, including that graph.

The others are done the same way.

[Guest]

The domain also includes x and y both negative (in the third quadrant) and above the branch of xy= 1 in that quadrant.

[Guest]

The domain also includes x and y both negative (in the third quadrant) and above the branch of xy= 1 in that quadrant.

Actually that's the fourth quadrant, not the third.

[Guest]

No, in the fourth quadrant x is positive. x and y are both negative in the third quadrant.