growth rate help calculus

Question

Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.

Answer 1

You need to find lim x>∞ of f(x) / g(x).

If this is a finite constant they grow at the same rate

Clearly f(x) / g(x) = 2000 / 200 = 10 which is a finite constant, proving the required result