Find the domain of continuity of this function

[chrisy2012]

Homework Statement

x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2)
find the domain of continuity

Homework Equations

none

The Attempt at a Solution

I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf)
but the professor then asked for the "domain of continuity" and asked us to "carefully explain", i don't know how that is different from the domain i found.

 

[Mark44]

Homework Statement

x*sin(sqrt(x^2+y^2))/sqrt(x^2+y^2)
find the domain of continuity

Homework Equations

none

The Attempt at a Solution

I found the domain, which is x^2+y^2 > 0 and since x^2 >= 0 and y^2 >= 0 therefore the domain is (-inf,0) (0,inf)

That's not the domain. As you have it, the domain is all of the real line except 0. Your function has a domain that is two-dimensional; i.e., the domain is actually some subset of R².

but the professor then asked for the "domain of continuity" and asked us to "carefully explain", i don't know how that is different from the domain i found.

 

[chrisy2012]

That's not the domain. As you have it, the domain is all of the real line except 0. Your function has a domain that is two-dimensional; i.e., the domain is actually some subset of R².

sorry my mistake, What i meant to say is that the domain is the xy plane except for at point (0,0). But still, how is that different from "domain of continuity"?

 

[Mark44]

I'm not familiar with that term. Your function is defined at and continuous at every point in the plane, except (0, 0). I'm guessing that, in this case, the domain of continuity is the same as the domain.