The problem involves determining the domain of continuity for the function \( \frac{x \sin(\sqrt{x^2+y^2})}{\sqrt{x^2+y^2}} \). Participants are exploring the differences between the domain of the function and its domain of continuity.
The discussion is ongoing, with participants questioning the definitions and implications of the terms used. Some guidance has been offered regarding the nature of the function's continuity, but no consensus has been reached on the distinction between the domain and the domain of continuity.
Participants note that the function is defined in a two-dimensional space and that the point (0,0) is a critical area of discussion regarding continuity.
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.chrisy2012 said: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)
chrisy2012 said: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 said: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.