# Thread: A Couple Limit Problems

1. ## A Couple Limit Problems

1. lim x -> +infinity sqrt(9x^6 - x) / (x^3 + 1)

2. lim x -> +infinity sqrt(9x^2 + x) - 3x

Thanks a lot.

2. 1) $\lim_{x\to\infty}\frac{\sqrt{9x^6-x}}{x^3+1}=\lim_{x\to\infty}\frac{x^3\sqrt{9-\frac{1}{x^5}}}{x^3\left(1+\frac{1}{x^3}\right)}=\ lim_{x\to\infty}\frac{\sqrt{9-\frac{1}{x^5}}}{1+\frac{1}{x^3}}=3$

2) $\lim_{x\to\infty}(\sqrt{9x^2+x}-3x)=\lim_{x\to\infty}\frac{9x^2+x-9x^2}{\sqrt{9x^2+x}+3x}=\lim_{x\to\infty}\frac{x}{ x\left(\sqrt{9+\frac{1}{x}}+3\right)}=\frac{1}{6}$

3. Thanks for the help

Can you please explain how you factored out x^3 in the denominator of the 1st problem?

edit: never mind I see it now. Thanks a lot!