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As explained in Example 1.2.3 (right below the definition of limit), why does the function not have a limit as 9 x 1 By the way, when the function doesn't have a limit, we can say the limit Does Not Exist and we can write it this way: lim g(x) DNE x 1 Because you only need to let x approach 1 from one side Because there is a hole in the graph When x approaches 1 from the left, g approaches a different value than when x approaches 1 from the right. So since g does NOT approach a single value as x approaches 1 from both sides, the limit doesn't exist. Because the graph of g is made up of different functions

As explained in Example 1.2.3 (right below the definition of limit), why does the function not have a limit as 9 x 1 By the way, when the function doesn't have a limit, we can say the limit Does Not Exist and we can write it this way: lim g(x) DNE x 1 Because you only need to let x approach 1 from one side Because there is a hole in the graph When x approaches 1 from the left, g approaches a different value than when x approaches 1 from the right. So since g does NOT approach a single value as x approaches 1 from both sides, the limit doesn't exist. Because the graph of g is made up of different functions

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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As explained in Example 1.2.3 (right below the definition of limit), why does the function not have a limit as X 9 1 By the way, when the function doesn't have a limit, we can say the limit Does Not Exist and we can write it this way: lim g(x) DNE x-1 Because you only need to let x approach 1 from one side Because there is a hole in the graph When x approaches 1 from the left, g approaches a different value than when x approaches 1 from the right. So since g does NOT approach a single value as x approaches 1 from both sides, the limit doesn't exist. Because the graph of g is made up of different functions
Transcribed Image Text:As explained in Example 1.2.3 (right below the definition of limit), why does the function not have a limit as X 9 1 By the way, when the function doesn't have a limit, we can say the limit Does Not Exist and we can write it this way: lim g(x) DNE x-1 Because you only need to let x approach 1 from one side Because there is a hole in the graph When x approaches 1 from the left, g approaches a different value than when x approaches 1 from the right. So since g does NOT approach a single value as x approaches 1 from both sides, the limit doesn't exist. Because the graph of g is made up of different functions
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