For which pair of functions f(x) and g(x) below will the lim f(x)/g(x)equal 0

Question

x-infinity
f(x) e^x; g(x) = x^3
f(x) x^5; g(x) = e^x
f(x) x^3; g(x) = ln(x)
f(x) x^negative 2; g(x) = e^negative x

Answer 1

exponentials grow faster than any power.

So, x^5/e^x -> 0

consider using l'Hospital's Rule. After 5 times, the limit is

120/e^x -> 0