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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![**Educational Website Content**
**Topic: Identifying Function, Variable, and Limit in a Given Limit Expression**
---
**Exercise:**
In the following limit expression, identify the function \( f(x) \), the variable \( a \), and the limit \( L \):
\[ \lim_{{x \to 3}} (-x + 2) = -1 \]
**Choices:**
Select the correct answer below:
1. \( f(x) = -x + 2; \, a = -1; \, L = 3 \)
2. \( f(x) = -x + 3; \, a = -1; \, L = 3 \)
3. \( f(x) = -x + 3; \, a = 3; \, L = -1 \)
4. \( f(x) = -x + 2; \, a = 3; \, L = -1 \)
---
**Explanation:**
To solve the given problem, compare the limit expression \(\lim_{{x \to 3}} (-x + 2) = -1\) with the general form \(\lim_{{x \to a}} f(x) = L\). The aim is to find the function \(f(x)\), the value \(a\) at which the limit is computed, and the limit \(L\).
Upon comparison, we can discern that:
- \( f(x) = -x + 2 \)
- \( a = 3 \)
- \( L = -1 \)
Thus, the fourth option \( f(x) = -x + 2; \, a = 3; \, L = -1 \) is the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18395f57-75e3-4bdb-980a-ed8850989594%2Ff9b3dd73-b704-4041-81bf-7b6173d29ba5%2F6vft9kv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
**Topic: Identifying Function, Variable, and Limit in a Given Limit Expression**
---
**Exercise:**
In the following limit expression, identify the function \( f(x) \), the variable \( a \), and the limit \( L \):
\[ \lim_{{x \to 3}} (-x + 2) = -1 \]
**Choices:**
Select the correct answer below:
1. \( f(x) = -x + 2; \, a = -1; \, L = 3 \)
2. \( f(x) = -x + 3; \, a = -1; \, L = 3 \)
3. \( f(x) = -x + 3; \, a = 3; \, L = -1 \)
4. \( f(x) = -x + 2; \, a = 3; \, L = -1 \)
---
**Explanation:**
To solve the given problem, compare the limit expression \(\lim_{{x \to 3}} (-x + 2) = -1\) with the general form \(\lim_{{x \to a}} f(x) = L\). The aim is to find the function \(f(x)\), the value \(a\) at which the limit is computed, and the limit \(L\).
Upon comparison, we can discern that:
- \( f(x) = -x + 2 \)
- \( a = 3 \)
- \( L = -1 \)
Thus, the fourth option \( f(x) = -x + 2; \, a = 3; \, L = -1 \) is the correct answer.
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