15 Nov
2013
15 Nov
'13
11:23 a.m.
Such examples, like f(x,y) = (x^2 - y^2)/(x^2 + y^2) (= cos(2θ)), are in a lot of textbooks, like Little Rudin (as of 1965), at least in the exercises. But I don't think most people would consider the point approached by the domain points (like (0,0) in the above example) as being part of the domain. --Dan
It actually is possible for a rational function OF SEVERAL VARIABLES to be discontinuous. I.e. different limits as you approach a 0/0 point from different directions. Little known fact.