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EXAMPLE 3 Use this definition of a right-hand limit to prove the following limit. lim V = 0 SOLUTION 1. Guessing a value for 6. Let e be a given positive number. Here a= and L- 0 , so we want to find a number ô such that if o 0, let ô = 0 . If o < x < ô, then IV - 01 < E. so

EXAMPLE 3 Use this definition of a right-hand limit to prove the following limit. lim V = 0 SOLUTION 1. Guessing a value for 6. Let e be a given positive number. Here a= and L- 0 , so we want to find a number ô such that if o 0, let ô = 0 . If o < x < ô, then IV - 01 < E. so

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXAMPLE 3 Use this definition of a right-hand limit to prove the following limit. lim Vx = 0 1. Guessing a value for ô. Let ɛ be a given positive number. Here a = , so we want to find a number ô such that SOLUTION and L = 0 if 0 < x< 6 then that is, if 0 < x< 8 then or, raising both sides of the inequality to the sixth power, we get if 0 < x< 8 then This suggests we should choose ô = ° 2. Showing that this ô works. Given e > 0, let ô =° . If 0 <x < 6, then IVA - 01 < E. so
Transcribed Image Text:EXAMPLE 3 Use this definition of a right-hand limit to prove the following limit. lim Vx = 0 1. Guessing a value for ô. Let ɛ be a given positive number. Here a = , so we want to find a number ô such that SOLUTION and L = 0 if 0 < x< 6 then that is, if 0 < x< 8 then or, raising both sides of the inequality to the sixth power, we get if 0 < x< 8 then This suggests we should choose ô = ° 2. Showing that this ô works. Given e > 0, let ô =° . If 0 <x < 6, then IVA - 01 < E. so
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