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
![**Limit of a Function**
In this example, we are asked to find the limit of the function as \( x \) approaches \(-1\). The mathematical notation for this is:
\[
\lim_{x \to -1} (9x + 1)^2
\]
This notation indicates that we need to evaluate the behavior of the function \((9x + 1)^2\) as \( x \) gets arbitrarily close to \(-1\).
**Step-by-Step Solution:**
1. **Substitute \(x = -1\) into the function:**
\[
9(-1) + 1 = -9 + 1 = -8
\]
2. **Square the result:**
\[
(-8)^2 = 64
\]
Thus, the limit is:
\[
\lim_{x \to -1} (9x + 1)^2 = 64
\]
**Conclusion**
The value of the limit is \(64\). This indicates that as \(x\) approaches \(-1\), the value of \((9x + 1)^2\) approaches \(64\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2133091-a753-411c-beef-444bf7f4574e%2Fc46ace3f-52a5-481a-97be-fce694536915%2F0gqw9qb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Limit of a Function**
In this example, we are asked to find the limit of the function as \( x \) approaches \(-1\). The mathematical notation for this is:
\[
\lim_{x \to -1} (9x + 1)^2
\]
This notation indicates that we need to evaluate the behavior of the function \((9x + 1)^2\) as \( x \) gets arbitrarily close to \(-1\).
**Step-by-Step Solution:**
1. **Substitute \(x = -1\) into the function:**
\[
9(-1) + 1 = -9 + 1 = -8
\]
2. **Square the result:**
\[
(-8)^2 = 64
\]
Thus, the limit is:
\[
\lim_{x \to -1} (9x + 1)^2 = 64
\]
**Conclusion**
The value of the limit is \(64\). This indicates that as \(x\) approaches \(-1\), the value of \((9x + 1)^2\) approaches \(64\).
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