I have been examining a function $f(r,\theta,\phi)$ where $f(r,\theta ,\phi)=\frac {1}{r\sin \theta}$ for $\theta \gt \pi /4$ $\;$ and $\;$ $f(r,\theta ,\phi) = 0$ for $\theta \lt \pi /4$. I am interested where this function is infinite and discontinuous.
We are working with the spherical coordinates. And if we are looking at $r\sin \theta$ as one entity it coresponds to $y$ axis, I think.
The singularity is of course at $r =0$ and for $\theta = 0$ we got $f = 0$ if $r$ isn't zero. But what if I get the $\theta \pi /4$ and $r \to 0$ limit? Is it also $f =0$?
For $\theta \gt \pi /4$ I think that for $r \to 0$ the function is infinite at that point. At $r = 0 $ the function is discontinous, right?
I know those limit question are actually trivial, but I am confusing those terms and i got two variables.