Answer
$\lim\limits_{x \to \infty}\frac{5x^3+1}{10x^3-3x^2+7} = \frac{1}{2}$
Work Step by Step
We look at the term with the highest degre in the numerator and denominator, as these will be the only values that have any significance when x approaches infinity.
$\lim\limits_{x \to \infty} \frac{5x^3+1}{10x^3-3x^2+7} = \lim\limits_{x \to \infty}\frac{5x^3}{10x^3} = \lim\limits_{x \to \infty}\frac{1}{2} = \frac{1}{2}$
