Calculus: Early Transcendentals
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ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![### Evaluating the Limit of a Function from a Graph
**Graph Description**
The graph presented displays the function \( f(x) \). The x-axis ranges from -10 to 10, while the y-axis ranges from -10 to 10 as well.
Key points to observe in the graph:
1. There is a curve with notable points at:
- \( (4, 5) \): An open circle indicating that \( f(4) \) is undefined.
- \( (5, -5) \): A closed circle indicating that \( f(5) = -5 \).
2. The curve approaches the point \( (5, -5) \) from both the left and right sides, suggesting the behavior of the function around \( x = 5 \).
3. From the graph, it is noticeable that as \( x \) approaches 5 from the right side (\( x \to 5^+ \)), the function \( f(x) \) tends to the point where \( y = -5 \).
**Task**
Given the graph of \( f(x) \) shown above, evaluate:
\[ \lim_{{x \to 5^+}} f(x) \]
**Solution**
From the graph, as \( x \) approaches 5 from the right side,
\[ \lim_{{x \to 5^+}} f(x) = -5 \]
*Note:* If the limit did not exist, you would enter ∅.
Use this graph to visually understand how limits work and how to evaluate them based on the behavior of the function near the point of interest.
**Practice**
Try to determine the following limits based on the same graph:
\[ \lim_{{x \to 4^+}} f(x) \]
\[ \lim_{{x \to 4^-}} f(x) \]
\[ \lim_{{x \to 6}} f(x) \]](https://content.bartleby.com/qna-images/question/b47bac88-cba5-40e5-9f3f-db7316eb95a3/68edb1d7-16de-4594-8e9b-c4649f31ea71/g4nq9g_processed.jpeg)
Transcribed Image Text:### Evaluating the Limit of a Function from a Graph
**Graph Description**
The graph presented displays the function \( f(x) \). The x-axis ranges from -10 to 10, while the y-axis ranges from -10 to 10 as well.
Key points to observe in the graph:
1. There is a curve with notable points at:
- \( (4, 5) \): An open circle indicating that \( f(4) \) is undefined.
- \( (5, -5) \): A closed circle indicating that \( f(5) = -5 \).
2. The curve approaches the point \( (5, -5) \) from both the left and right sides, suggesting the behavior of the function around \( x = 5 \).
3. From the graph, it is noticeable that as \( x \) approaches 5 from the right side (\( x \to 5^+ \)), the function \( f(x) \) tends to the point where \( y = -5 \).
**Task**
Given the graph of \( f(x) \) shown above, evaluate:
\[ \lim_{{x \to 5^+}} f(x) \]
**Solution**
From the graph, as \( x \) approaches 5 from the right side,
\[ \lim_{{x \to 5^+}} f(x) = -5 \]
*Note:* If the limit did not exist, you would enter ∅.
Use this graph to visually understand how limits work and how to evaluate them based on the behavior of the function near the point of interest.
**Practice**
Try to determine the following limits based on the same graph:
\[ \lim_{{x \to 4^+}} f(x) \]
\[ \lim_{{x \to 4^-}} f(x) \]
\[ \lim_{{x \to 6}} f(x) \]
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