Let , , and be monic polynomials of degrees , , and , respectively, where , , and are…

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

Problem

Let

f

g

, and

h

be monic polynomials of degrees

m

n

, and

p

, respectively, where

m

n

, and

p

are prime numbers and

m<n<p

. If

\lim_{x\to\infty}\frac{h(x)}{x^{13}}=1

and

L=\lim_{x\to\infty}\frac{h(6x)}{f(2x)\cdot g(3x)}

is non-zero and finite, then

L

equals (a)

1

(b)

9\times2^{13}

(c)

9\times2^{11}

(d)

4\times3^{11}