calculus question

Question

What does  show? (4 points)

	g(x) grows faster than f(x) as x goes to infinity.
	f(x) and g(x) grow at the same rate as x goes to infinity.
	f(x) grows faster than g(x) as x goes to infinity.
	L'Hôpital's Rule must be used to determine the true limit value.

Answer 1

g(x) grows faster than f(x) as x goes to infinity,

because lim(f(x)/g(x)) = 0 is the formal definition of

"g(x) grows faster than f(x) as x goes to infinity".

L'Hopital's Rule is not needed, because that is used to calculate lim(f(x)/g(x)), but that is already given.

And L'Hopital's Rule does not necessarily apply as it has requirements, which the problem does not mention.