Let , where and are nonzero real numbers and and are any real numbers. Which of the…

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

g(x)=\dfrac{ax^{3}+bx^{2}}{cx^{3}+d}

, where

a

and

c

are nonzero real numbers and

b

and

d

are any real numbers. Which of the following statements about

L=\displaystyle\lim_{x\to\infty} g(x)

is always true? (a)

L=\dfrac{a+b}{c+d}

(b)

L=\dfrac{a}{c}

(c)

L=0

(d)

L

does not exist because the numerator and denominator both approach infinity