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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q2
![### Problem Statement
2. Evaluate the following limits:
\[ \lim_{x \to -2} 7x + 3. \]
### Explanation
The expression asks for the evaluation of the limit of the linear function \(7x + 3\) as \(x\) approaches \(-2\). In this context, since \(7x + 3\) is a polynomial function, it is continuous everywhere. Therefore, the limit can be found by direct substitution of \(-2\) into the expression.
### Solution
1. Substitute \(x = -2\) into the equation:
\[
7(-2) + 3 = -14 + 3 = -11.
\]
Therefore, the limit is \(-11\).
### Additional Notes
For linear functions like \(7x + 3\), limits can be evaluated directly by substitution because these functions are continuous across their entire domain. This provides a straightforward and efficient approach to finding limits for polynomial functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e422df6-8ba9-49fe-b437-5f3f14519581%2Fc0340a25-41b3-457a-b49f-0c343453da2c%2Fqacz16j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
2. Evaluate the following limits:
\[ \lim_{x \to -2} 7x + 3. \]
### Explanation
The expression asks for the evaluation of the limit of the linear function \(7x + 3\) as \(x\) approaches \(-2\). In this context, since \(7x + 3\) is a polynomial function, it is continuous everywhere. Therefore, the limit can be found by direct substitution of \(-2\) into the expression.
### Solution
1. Substitute \(x = -2\) into the equation:
\[
7(-2) + 3 = -14 + 3 = -11.
\]
Therefore, the limit is \(-11\).
### Additional Notes
For linear functions like \(7x + 3\), limits can be evaluated directly by substitution because these functions are continuous across their entire domain. This provides a straightforward and efficient approach to finding limits for polynomial functions.
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