e the graph below to answer the question below: 4 y = f(r) 1 1. 2. 4 Find lim f(r). Be sure to read this as a one-sided limit. None of the other answers is correct. 2
e the graph below to answer the question below: 4 y = f(r) 1 1. 2. 4 Find lim f(r). Be sure to read this as a one-sided limit. None of the other answers is correct. 2
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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![### Understanding One-Sided Limits with a Graph
#### Graph Description
The provided graph shows a piecewise function \( y = f(x) \) with distinct segments and points marked.
1. **Visual Segments:**
- A horizontal line at \( y = 2 \) from \( x = 0 \) to barely before \( x = 1 \) with an open circle at \( x = 1 \).
- A semicircular arc rises from just after \( x = 1 \) to \( x = 2 \), reaching a peak, then descends to just before \( x = 3 \). Both ends of the semicircle have open circles.
- A horizontal line from \( x = 3 \) to \( x = 4 \) with an open circle at both ends.
- A line segment slants upwards beginning at an open circle at \( x = 4 \), implying a continuation beyond the shown section.
2. **Gaps and Open Circles:**
- There are open circles at \( x = 1 \), \( x = 3 \), and \( x = 4 \) indicating that the function is not defined at these exact points.
#### Problem
You're asked to find the one-sided limit as \( x \) approaches 1 from the right:
\[ \lim_{{x \to 1^{+}}} f(x) \]
**Note:** The graph shows that as \( x \) approaches 1 from the positive side, the value of \( f(x) \) approaches the starting point of the semicircle, which appears to be around \( y = 3 \).
#### Answer Choices
- None of the other answers is correct.
- 2
- 3
- 1
- 4
#### Correct Answer
The correct answer is \( 3 \). As \( x \) approaches 1 from the right, \( f(x) \) approaches the y-value at the beginning of the semicircle, which is \( y = 3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c72f5a5-765b-4af8-8c83-eae60846a923%2Fd01f5861-8560-4cc8-bcf8-9c2b3313881b%2Ffooy8gt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding One-Sided Limits with a Graph
#### Graph Description
The provided graph shows a piecewise function \( y = f(x) \) with distinct segments and points marked.
1. **Visual Segments:**
- A horizontal line at \( y = 2 \) from \( x = 0 \) to barely before \( x = 1 \) with an open circle at \( x = 1 \).
- A semicircular arc rises from just after \( x = 1 \) to \( x = 2 \), reaching a peak, then descends to just before \( x = 3 \). Both ends of the semicircle have open circles.
- A horizontal line from \( x = 3 \) to \( x = 4 \) with an open circle at both ends.
- A line segment slants upwards beginning at an open circle at \( x = 4 \), implying a continuation beyond the shown section.
2. **Gaps and Open Circles:**
- There are open circles at \( x = 1 \), \( x = 3 \), and \( x = 4 \) indicating that the function is not defined at these exact points.
#### Problem
You're asked to find the one-sided limit as \( x \) approaches 1 from the right:
\[ \lim_{{x \to 1^{+}}} f(x) \]
**Note:** The graph shows that as \( x \) approaches 1 from the positive side, the value of \( f(x) \) approaches the starting point of the semicircle, which appears to be around \( y = 3 \).
#### Answer Choices
- None of the other answers is correct.
- 2
- 3
- 1
- 4
#### Correct Answer
The correct answer is \( 3 \). As \( x \) approaches 1 from the right, \( f(x) \) approaches the y-value at the beginning of the semicircle, which is \( y = 3 \).
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