#### Answer

$$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}=\infty$$

#### Work Step by Step

$$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}$$
As $r\to 9$, $\frac{\sqrt r}{(r-9)^4}$ approaches $\frac{\sqrt9}{(9-9)^4}=\frac{3}{0}=\infty$
Therefore, $$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}=\infty$$
*NOTE: In this situation, since we cannot simplify the denominator so that it would not be 0 when we plug in the number, we must accept the fact that this function would approach infinity as $r\to9$.