Help needed with math, please and thank you

Question

What does  show?

Options:

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

Answer 1

f(x) and g(x) could be any function with a dependent variable x in it, for example:

f(x) = x² + 2x + 3

g(x) = x⁴ + x²

If x is approaching ∞, then if you substitute 1,3,5...so on into x for each equation above, g(x) will be much greater than f(x) as you substitute increasing values.

So when it says the limit approaches 0 for f(x)/g(x) as x is approaching ∞, it means g(x) >> f(x) to the point where f(x) is essentially 0 compared to g(x)