Evaulate $\lim_{x\to\infty}\frac{3x^2-36x+12}{5x^2+113x-2}$ Question:  Find the limit, $$\lim_{x\to\infty}\frac{3x^2-36x+12}{5x^2+113x-2}$$
The limit should be $\frac{3}{5}$ since when $x$ approaches infinity since $\frac{3*\infty^2}{5*\infty^2}$ and infinity squared cancels out.  Am I correct?

HINT:
$$\frac{3x^2-36x+12}{5x^2+113x-2} =\frac{3-\frac{36}x+\frac{12}{x^2}}{5+\frac{113}x-\frac2{x^2}}$$

Alternatively  putting $\frac1x=y$ as $x\to\infty,y\to0$
$$\lim_{x\to\infty}\frac{3x^2-36x+12}{5x^2+113x-2} =\lim_{y\to0}\frac{3-36y+12y^2}{5+113y-2y^2} $$
