Chapter 11.1, Problem 83E

(a)

To determine

To explain: The reason behind for finding $\underset{x\to \infty }{\lim }\left[\frac{p\left(x\right)}{q\left(x\right)}\right]$ by using the rule “If the degree of $p\left(x\right)$ is less than the degree of $q\left(x\right)$, the limit is 0”.

(b)

To determine

To explain: The reason behind finding $\underset{x\to \infty }{\lim }\left[\frac{p\left(x\right)}{q\left(x\right)}\right]$ by using the rule “If the degree of $p\left(x\right)$ is equal to the degree of $q\left(x\right)$, the limit is $\frac{A}{B}$, where A and B are the leading coefficients of $p\left(x\right)$ and $q\left(x\right)$, respectively”.

(c)

To determine

To explain: The reason behind finding $\underset{x\to \infty }{\lim }\left[\frac{p\left(x\right)}{q\left(x\right)}\right]$ by using the rule “If the degree of $p\left(x\right)$ is greater than the degree of $q\left(x\right)$, the limit is $\infty \text{ or }-\infty$”.