I do not understand the second part of the following question. Can someone please explain it to me. Thanks
Find all points in the plane where f is not defined. Is it possible to extend the domain of f to the entire plane (by defining values of f(x,y) at points where it it currently undefined) in such a way that the 'new' function is continuous on the entire plane?
See the attached gif (click on function and Answer.gif) for the Function and 1st part answer of the question. The 2nd part answer of the question is these points can be added to the domain of f(x,y) by defining f(x,y)=2y.
Function: f(x,y) = (x^2  y^2)/(x  y)
Answer: 1st part {x, y E R^2  x=y}
Find all points in the plane where f is not defined. Is it possible to extend the domain of f to the entire plane (by defining values of f(x,y) at points where it it currently undefined) in such a way that the 'new' function is continuous on the entire plane?
See the attached gif (click on function and Answer.gif) for the Function and 1st part answer of the question. The 2nd part answer of the question is these points can be added to the domain of f(x,y) by defining f(x,y)=2y.
Function: f(x,y) = (x^2  y^2)/(x  y)
Answer: 1st part {x, y E R^2  x=y}
Attachments

1,004 bytes Views: 12

1.1 KB Views: 6
Last edited: