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0 0 1 ,0 , forms Evaluate the following limits. Check your

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

Solution for problem 41RE 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 41RE

? 0 0 1 ,0 ,? forms ?Evaluate the following limits. Check your results by graphing. lim(1? ) 3 x x?? x

Step-by-Step Solution:

Solution Step 1 3 x In this problem we have to evaluate lim (1 ) x x By direct substitution of limit, we get 3 x x(1 )x= 1 Thus lim (1 ) has the indeterminate form 1 . x x To evaluate this limit we will be using the following two steps: Assume limf(x) g(x)has the indeterminate form 0 1 , . 0 xa 0 1. Evaluate L = limg(x)ln f(x).This limit can often be put in the form 0or both of which xa can be handled by l’hopital’s rule. g(x) L 2. Then limf(x) = e xa l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim xa g(x)= 0or lxa g(x)= ± Where a can be any real number, infinity or negative infinity. In these cases we have lim f(x)= lim f(x) xa g(x) xa g(x)

Step 2 of 4

Chapter 4, Problem 41RE is Solved
Step 3 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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0 0 1 ,0 , forms Evaluate the following limits. Check your