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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![### Calculating Limits: An Example
Let's explore calculating a limit example based on a provided graph. The specific limit we are trying to find is:
\[ \lim_{{x \to 1^+}} f(x) \]
#### The Graph
Before we determine the limit, let's analyze the graph of the function \( f(x) \). The graph displays how \( f(x) \ behaves as \( x \) approaches 1 from the right.
#### Key Features of the Graph:
- The x-axis ranges from around \(-6\) to \(6\).
- The y-axis ranges from around \(-6\) to \(6\).
Let's enumerate the behaviors we observe around \( x = 1 \):
1. **From the Right ( \( x \to 1^+ \) ):**
- As \( x \) approaches 1 from the right side, the value of \( f(x) \) trends towards \( 1 \).
- There is a prominent point on the graph around \( x = 1 \) where \( f(x) \) equals \( 1 \).
#### Multiple Choice Question
What is the limit of the function \( f(x) \) as \( x \) approaches 1 from the right?
A. -1
B. 1
C. 3
D. The limit does not exist
Based on our analysis of the graph:
The limit \( \lim_{{x \to 1^+}} f(x) = 1 \).
Therefore, the correct answer is:
B. 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd9966fd-53bb-4986-9621-0cf929ae8043%2Fb500b420-2f9e-432f-b4c7-32effa7be38f%2Fftzxxj_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating Limits: An Example
Let's explore calculating a limit example based on a provided graph. The specific limit we are trying to find is:
\[ \lim_{{x \to 1^+}} f(x) \]
#### The Graph
Before we determine the limit, let's analyze the graph of the function \( f(x) \). The graph displays how \( f(x) \ behaves as \( x \) approaches 1 from the right.
#### Key Features of the Graph:
- The x-axis ranges from around \(-6\) to \(6\).
- The y-axis ranges from around \(-6\) to \(6\).
Let's enumerate the behaviors we observe around \( x = 1 \):
1. **From the Right ( \( x \to 1^+ \) ):**
- As \( x \) approaches 1 from the right side, the value of \( f(x) \) trends towards \( 1 \).
- There is a prominent point on the graph around \( x = 1 \) where \( f(x) \) equals \( 1 \).
#### Multiple Choice Question
What is the limit of the function \( f(x) \) as \( x \) approaches 1 from the right?
A. -1
B. 1
C. 3
D. The limit does not exist
Based on our analysis of the graph:
The limit \( \lim_{{x \to 1^+}} f(x) = 1 \).
Therefore, the correct answer is:
B. 1
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