So, anyone wants to solve maths problems this weekend? Here's your chance!
It's not exactly rocket science, but I'm not sure if there's a solution to the following problem:
f(x,y) = arctan(|y/x|) is a continuous function. Can it be extended to be a continuous function defined in all of R^2?
I'm thinking you could define it as for example:
f(x,y) = arctan(|y/x|) when x!=0 and
(π/2) - arctan(|x/y|) when x = 0 && y!=0
But it is still not continuous in (0,0). If I approach (0,0) along the x-axis, f approaches 0, while it seems to approach (π/4) if I go diagonally (t,t) -> (0,0). So is the answer simply no, or am I missing something? Thoughts?
P.S Yes this is for a university course, but cooperation is encouraged by the professor
