How to Solve a Limit Problem Involving Square Roots and a Constant

[synergix]

Homework Statement

Lim sqrt(r)/(r-9)⁴
r->9

The Attempt at a Solution

I haven't been able to get started on this one I first tried to factor the bottom but I don't know how to or if that is even the right way to solve this problem. I am thinking maybe I have to multiply the bottom out but that seems a bit tedious.

is it sufficient to simply test from the left and right in order to get my answer?

 

[lanedance]

this limit will be infinite, just by inspection

the numerator will be 3, whilst the denominator tends to 0

if you want to show it is unbounded, pick any positive number N, then show you can chose d, such that for |r-9|<d, then F(r) > N

but in answer to your question it is sufficient to show the limit is the same from the left & right