Comparing growth rates? Determine which of the two functions grows faster, or state that they have comparable growth rates. 10xand ln x
Solution Step 1 In this problem we have to determine which of the two functions 10xand ln x, grows faster than the other otherwise we have to state the comparable growth rates. Suppose f and g are functions such that lim f(x) = , lim g(x) = x x g(x) Enough to prove: lim f(x)= 0which means f grows faster than g as x x l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim g(x)= 0 or lim g(x)= ± xa xa Where a can be any real number, infinity or negative infinity. f(x) (x) In these cases we have lim g(x)= lim g(x) xa xa
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Comparing growth rates? Determine which of the two functions grows faster, or state that they have comparable growth rates. 10xand ln x” is broken down into a number of easy to follow steps, and 22 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 42RE from chapter: 4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 42RE from 4 chapter was answered, more than 325 students have viewed the full step-by-step answer. This full solution covers the following key subjects: growth, Rates, grows, faster, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.