Explain why the following rules can $be$ used $to$ find $\underset{x+-}{lim}[\frac{p(x)}{q(x)}].$

$a.If$ the degree $ofp(x)is$ less than the degree $ofq(x)$ the $limitis0.$

$b.If$ the degree $ofp(x)is$ equal $to$ the degree $ofq(x)$ the $limitis\frac{A}{B}$ where A and $B$ are the leading coefficients $ofp(x)$

and $q(x)$ and respectively.

$c.If$ the degree $ofp(x)is$ greater than the degree $ofq(x)$ the $limitisor-.$

$C.$ Since the degree $ofp(x)is$ less than the degree $ofq(x),p(x)$ will approach $+-$ much faster than $q(x),$ and

$asp(x)$ and $q(x)$ become larger, the ratio $\frac{p(x)}{q(x)}$ will approach $0.$

$b.$ Choose the correct answer below.

$A.Asx$ becomes large, the term with the highest exponent $in$ the numerator and the term with the highest

exponent $in$ the denominator become the dominant terms. $In$ the $limit$ the other terms become negligible, and

the $limitof$ the rational function $is$ the ratio $of$ the coefficients $of$ the highest terms.

$B.Asx$ becomes large, the term with the lowest exponent $in$ the numerator and the term with the lowest exponent

$in$ the denominator become the dominant terms. $In$ the $limit$ the other terms become negligible, and the $limitof$

the rational function $is$ the ratio $of$ the coefficients $of$ the lowest terms.

$C.Asx$ becomes large, the term with the highest exponent $in$ the numerator and the term with the lowest exponent

$in$ the denominator become the dominant terms. $In$ the $limit$ the other terms become negligible, and the $limitof$

the rational function $is$ the ratio $of$ the coefficient $of$ the highest term $in$ the numerator and the coefficient $of$ the

lowest term $in$ the denominator.