Comparing growth rates? Determine which of the two functions grows faster, or state x that they have comparable growth rates. e and 3

Solution Step 1 x In this problem we have to determine which of the two functions e and 3 , grows faster than the other otherwise we have to state the comparable growth rates. Suppose f and gare functions such that xf(x) = , limx) = Enough to prove:lim f(x)= 0which means ggrows faster than f as x x g(x) l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim g(x)= o0 lim g(x)= ± xa xa Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim xa g(x)= xa gx)