Mathematics

Problem

Let

f, g

and

h

be monic polynomials of degree

m, n

and

p

respectively where

m, n

and

p

are prime numbers (

m < n < p

). If

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

and

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

is non-zero finite then

L

equals (a) 1 (b)

9 \times 2^{13}

(c)

9 \times 2^{11}

(d)

4 \times 3^{11}