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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### Problem: Limit Determination from a Graph
Given the graph of \( f(x) \), determine
\[ \lim_{{x \to 1}} f(x) \]
**Graph Explanation:**
The graph features a line and a point plotted on a Cartesian coordinate system.
- The x-axis ranges from -3 to 3.
- The y-axis ranges from 0 to 5.
- A line passes through points (0, 1), (1, 3), and (2, 4).
There is a noticeable dot at the coordinate (1, 2).
**Question Options:**
- \( \bigcirc \) 2
- \( \bigcirc \) 4
- \( \bigcirc \) Does not exist
- \( \bigcirc \) None of the above
---
From the graph, we observe how the function behaves as it approaches \( x = 1 \):
- As \( x \) approaches 1 from either direction, the value of \( f(x) \) is approaching 3.
**Conclusion:**
The limit \( \lim_{{x \to 1}} f(x) = 3 \). However, this value is not present among the given choices. Therefore, the correct choice is:
- \( \bigcirc \) None of the above
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc953914a-58e5-446d-8333-dea1ae17cc05%2Fe79d70c8-0564-4a75-b7d2-48cfd2f64c85%2Fre3gx8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Problem: Limit Determination from a Graph
Given the graph of \( f(x) \), determine
\[ \lim_{{x \to 1}} f(x) \]
**Graph Explanation:**
The graph features a line and a point plotted on a Cartesian coordinate system.
- The x-axis ranges from -3 to 3.
- The y-axis ranges from 0 to 5.
- A line passes through points (0, 1), (1, 3), and (2, 4).
There is a noticeable dot at the coordinate (1, 2).
**Question Options:**
- \( \bigcirc \) 2
- \( \bigcirc \) 4
- \( \bigcirc \) Does not exist
- \( \bigcirc \) None of the above
---
From the graph, we observe how the function behaves as it approaches \( x = 1 \):
- As \( x \) approaches 1 from either direction, the value of \( f(x) \) is approaching 3.
**Conclusion:**
The limit \( \lim_{{x \to 1}} f(x) = 3 \). However, this value is not present among the given choices. Therefore, the correct choice is:
- \( \bigcirc \) None of the above
---
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