Solution Found!
Comparing growth rates Determine which of the
Chapter 4, Problem 47RE(choose chapter or problem)
Determine which of the two functions grows faster, or state that they have comparable growth rates.
\(e^x\ and\ 3^x\)
Questions & Answers
QUESTION:
Determine which of the two functions grows faster, or state that they have comparable growth rates.
\(e^x\ and\ 3^x\)
ANSWER: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)