3-d continuity: find pts where arcsin(x^2+y^2) is continuous

[acpodgorski]

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

G(x, y) = arcsin(x^2 + y^2).

What effect would arcsin have on continuity, or any inverse for that matter? I know that the x^2+y^2 is a circle which would always be continuous....

 

[arthur ohlsten]

z=arc sin [x^2+y^2]
let x^2+y^2=R^2

z=arc sin R^2
sinz= R^2

then R must be 0<R<1 for sinz to be real

0<[x^2+y^2]<1 to be continuous.

I believe this is what your instructor requires.
Arthur

continuous means that you can trace the curve with your finger without removing your finger from the page.

 

[arthur ohlsten]

sorry I goofed
0<R^2<1
-1<R<1 answer

sorry
Arthur