Help needed with math, please and thank you

Question

Which of the following functions grows at the same rate as ?

Options:

1)	x
2)	x2
3)	x3
4)	x4

Answer 1

The same rate as x² because lim as x → ∞ of ratio (x⁴ + x)^1/2/x² = lim as x → ∞ of x²(1 + 1/x³)^1/2/x² =

lim as x → ∞ of (1 + 1/x³)^1/2 = (1 + 0)^1/2 = 1

Because answer is 2) or x²