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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![### Question on Limits from Graphs
Use the graph to determine whether each statement is true or false.
#### Statement:
\[ \lim_{{x \to -2^+}} f(x) = \lim_{{x \to -2^-}} f(x) \]
#### Graph Explanation:
The graph provided shows a coordinate plane with the x-axis ranging from -5 to 5 and the y-axis ranging from -3 to 5. The graph includes a piecewise function represented by different parts:
1. As \( x \) approaches -2 from the right (\( x \to -2^+ \)), the function \( f(x) \) approaches the value 3. This is indicated by the open circle at the point (−2, 3) on the graph.
2. As \( x \) approaches -2 from the left (\( x \to -2^- \)), the function \( f(x) \) approaches the value -1. This is indicated by the graph approaching the point (-2, -1) and a closed circle at the point (-2, -1).
### Multiple Choice Question:
**Is the given statement true or false?**
- False
- True](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc156cfcf-b572-4dd1-9c92-c49112da643d%2F31a65f13-8d71-47c7-b2e3-63a99caa3737%2Fex8ts5t_processed.png&w=3840&q=75)
Transcribed Image Text:### Question on Limits from Graphs
Use the graph to determine whether each statement is true or false.
#### Statement:
\[ \lim_{{x \to -2^+}} f(x) = \lim_{{x \to -2^-}} f(x) \]
#### Graph Explanation:
The graph provided shows a coordinate plane with the x-axis ranging from -5 to 5 and the y-axis ranging from -3 to 5. The graph includes a piecewise function represented by different parts:
1. As \( x \) approaches -2 from the right (\( x \to -2^+ \)), the function \( f(x) \) approaches the value 3. This is indicated by the open circle at the point (−2, 3) on the graph.
2. As \( x \) approaches -2 from the left (\( x \to -2^- \)), the function \( f(x) \) approaches the value -1. This is indicated by the graph approaching the point (-2, -1) and a closed circle at the point (-2, -1).
### Multiple Choice Question:
**Is the given statement true or false?**
- False
- True
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