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Solution: Comparing growth rates Determine which of the two

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 44RE Chapter 4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 44RE

Comparing growth rates? Determine which of the two functions grows faster, or state that they have comparable growth rates. ln xand log 10

Step-by-Step Solution:

Solution Step 1 In this problem we have to determine which of the two functions ln xand log x, grows fast10 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 Enough to prove:lim g(x) = 0which means f grows faster than gas x x f(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 = lim xa g(x) xa gx)

Step 2 of 2

Chapter 4, Problem 44RE is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solution: Comparing growth rates Determine which of the two