We need to look at what happens to top and to bottom as $r$ approaches $0$ from the right. The bottom behaves very nicely: as $r$ approaches $0$, $(r-9)^4$ approaches $(-9)^4$.
The top also behaves nicely: as $r$ approaches $0$ from the right, $\sqrt{r}$ approaches $0$.
So the quotient approaches $0/(-9)^4$, which is $0$.
Things get substantially more difficult when top and bottom both approach $0$. In that sort of situation, the analysis can be quite a bit harder to do.
Remark: You might wish to confirm this with some calculator experimentation. Pick a very small positive $r$, like $r=10^{-6}$. Calculate $\frac{\sqrt{r}}{(r-9)^4}$. You will find it is close to $0$.