Find a limit expression

Question

Use limit methods to determine which of the two given functions grows​ faster, or state that they have comparable growth rates.

x^7; e^0.03x

Answer 1

Always an exponential function grows faster than a polynomial. So in our case we have that the limit as x goes to infinity of (e^(0,03x))/(x^7) is infinity. To see this mathematically just use the Del' Hospital rule and differentiate 7 times. The numerator will always be an exponential function but the denominator will become just a constant.