Rational Function Limit at Infinity

Rational Function Limit at Infinity

For:

$$f(x)=\frac{P(x)}{Q(x)}$$

compare the degrees of $$P(x)$$ and $$Q(x)$$.

If:

$$\deg P<\deg Q$$

then:

$$\lim_{x\to\infty}\frac{P(x)}{Q(x)}=0$$

If:

$$\deg P=\deg Q$$

then:

$$\lim_{x\to\infty}\frac{P(x)}{Q(x)}=\frac{\text{leading coefficient of }P}{\text{leading coefficient of }Q}$$

Usage

- Used to quickly evaluate rational-function limits at infinity.