Give an example for the Limits of Function Values?

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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Give an example for the Limits of Function Values?

Expert Solution
Step 1

The limit of f(x) as x approaches x0 is L, and we write it as:

Calculus homework question answer, step 1, image 1

 

Step 2

Consider the following function:

Calculus homework question answer, step 2, image 1

and let x0 = 1

Clearly, the function is not defined for x0 = 1 as the denominator is 0 and also we get 0/0 form when we plug in 0

But we can calculate the limit at 1 as follows:

Calculus homework question answer, step 2, image 2

 

 

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