Let . For which ordered pair does exist and equal…

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

Problem

Let

g(x)=\dfrac{ax^{3}+bx^{2}+1}{x^{2}+3}

. For which ordered pair

(a,b)

does

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

exist and equal

6

? (a)

(6,0)

(b)

(6,6)

(c)

(0,6)

(d)

(0,-6)