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:**
5. Solve the inequality \(|y - 4| < 0.001\). (Report with decimals)
**Solution:**
To solve this inequality involving absolute values, we interpret it as two separate inequalities:
1. \(y - 4 < 0.001\)
2. \(y - 4 > -0.001\)
Solving the first inequality:
\[ y < 4 + 0.001 \]
\[ y < 4.001 \]
Solving the second inequality:
\[ y > 4 - 0.001 \]
\[ y > 3.999 \]
Combining these two inequalities, we find:
\[ 3.999 < y < 4.001 \]
So, the solution in decimal form is:
\[ y \in (3.999, 4.001) \]
This represents the range of values \(y\) can take to satisfy the given inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41a94607-ae05-49d2-a989-bd66a70c4a42%2F1dcc4f37-40c7-42ab-9946-dc5f3607a9a9%2F2va0eqa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
5. Solve the inequality \(|y - 4| < 0.001\). (Report with decimals)
**Solution:**
To solve this inequality involving absolute values, we interpret it as two separate inequalities:
1. \(y - 4 < 0.001\)
2. \(y - 4 > -0.001\)
Solving the first inequality:
\[ y < 4 + 0.001 \]
\[ y < 4.001 \]
Solving the second inequality:
\[ y > 4 - 0.001 \]
\[ y > 3.999 \]
Combining these two inequalities, we find:
\[ 3.999 < y < 4.001 \]
So, the solution in decimal form is:
\[ y \in (3.999, 4.001) \]
This represents the range of values \(y\) can take to satisfy the given inequality.
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