Here is the question...
Determine the points (x,y), if any, at which f(x,y) is not continuous.
Can someone please solve these and explain to me how to go about solving them? Thanks in advance.
x+y is continuous everywhere and so is so is continous everywhere. is continuous for all positive x (and "continuous from the right" at x= 0) so is continuous for all (x,y) such that x+y> 0. x+ y= 0 or y= -x is a line through (0,0) and (1,0) has 1+ 0> 0 so is continuous "above and to the right" of that line.
is continous for (x,y) "above and to the right" of the line y= -x and "continuous from above and to the right:" on that line.