Solution Found!
Comparing growth rates Determine which of the two
Chapter 4, Problem 43RE(choose chapter or problem)
Determine which of the two functions grows faster, or state that they have comparable growth rates.
\(x^{1/2}\ and\ x^{1/3}\)
Questions & Answers
QUESTION:
Determine which of the two functions grows faster, or state that they have comparable growth rates.
\(x^{1/2}\ and\ x^{1/3}\)
ANSWER:Solution Step 1 1/2 1/3 In this problem we have to determine which of the two functions x and x , grows faster than the other otherwise we have to state the comparable growth rates. Suppose f and gare functions such that limf(x) = , limg(x) = x x f(x) Enough to prove:lim x g(x)= which means f grows faster than gas x l'Hôpital's Rule: Suppose that we have one of the following cases, lim f(x)= or lim f(x)= ± xa g(x) 0 xa g(x) ± Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim g(x)= lim g(x) xa xa