Mathematics

Problem

x\to\infty

, consider the functions

f(x)=\ln x

and

g(x)=x^{1/3}

. Which of the following statements correctly describes their relative growth rates? a)

\displaystyle\lim_{x\to\infty}\frac{\ln x}{x^{1/3}}=\infty

, so

f

grows faster than

g

. b)

\displaystyle\lim_{x\to\infty}\frac{\ln x}{x^{1/3}}=1

, so

f

and

g

grow at the same rate. c)

\displaystyle\lim_{x\to\infty}\frac{\ln x}{x^{1/3}}=0

, so

g

grows faster than

f

. d)

\displaystyle\lim_{x\to\infty}\frac{\ln x}{x^{1/3}}=0

, so

f

grows faster than

g