What does limit as x goes to infinity of the quotient of f of x and g of x equals infinity show

Question

What does  show

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

b)f(x) and g(x) grow at the same rate as x goes to infinity.

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

d)L'Hôpital's Rule must be used to determine the true limit value.

Answer 1

The answer is c).

That limit is the formal definition of "f(x) grows faster than g(x) as x goes to infinity".

L'Hôpital's Rule does not apply for many reasons.