Answer
We can calculate the limit of rational functions as $x\to\pm\infty$ by dividing both numerator and denominator by the highest degree of $x$ in the denominator.
Work Step by Step
We can calculate the limit of rational functions as $x\to\pm\infty$ by dividing both numerator and denominator by the highest degree of $x$ in the denominator.
For example, calculate this limit: $$A=\lim_{x\to-\infty}\frac{x^2+1}{x^3-1}$$
The highest degree of $x$ in the denominator here is $x^3$, so we divide both numerator and denominator by $x^3$: $$A=\lim_{x\to-\infty}\frac{\frac{1}{x}+\frac{1}{x^3}}{1-\frac{1}{x^3}}=\frac{\lim_{x\to-\infty}\frac{1}{x}+\lim_{x\to-\infty}\frac{1}{x^3}}{\lim_{x\to-\infty}1-\lim_{x\to-\infty}\frac{1}{x^3}}$$
$$A=\frac{0+0}{1-0}=0$$
