# Homework Help: Limit as x goes to infinity (algebraic)

1. Oct 16, 2008

### mbisCool

1. The problem statement, all variables and given/known data
limx->infinity (x+2)/(sqrt(81x^2+15))

2. Relevant equations

3. The attempt at a solution
The only thing i could think of doing was rationalizing the denominator to get (x+2)sqrt(81x^2+15) / 81X^2+15 however im pretty sure this is the wrong route cause there doesnt seem to be anywhere to go from here.

Any help would be greatly apprciated :D the only problems i seem to ever have difficulty with are with roots in the numerator or denominator. any info in that regard would be of use as well.

2. Oct 16, 2008

### jacobrhcp

divide top and bottom by x and write an x inside the root

3. Oct 16, 2008

### mbisCool

what exactly do you mean by write an x inside the root. if i divide top and bottom by x i get ((x+2)/x) / ((sqrt(81x^2+15))/x). from here im stuck again

4. Oct 16, 2008

### mbisCool

alright its 1/9

5. Oct 16, 2008

### jacobrhcp

note that this trick generalizes to all rational polynomial limits to infinity, just divide by the highest factor.