Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places. 29 using differentials
Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places. 29 using differentials
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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![### Using Differentials to Approximate Values
In this exercise, we will use differentials to approximate the value of the given expression and then compare our estimate with the result obtained from a calculator. The goal is to round our answers to four decimal places for consistency and accuracy.
#### Given Expression
\( \sqrt{29} \)
#### Steps
1. **Approximation using Differentials**:
- We first approximate the value of the expression using differentials. This involves calculus techniques like linear approximation.
- Enter the result in the provided input box under the label "using differentials."
2. **Calculator Value**:
- Calculate the exact value using a calculator.
- For \( \sqrt{29} \), the calculator provides the value as 3.0723.
#### Comparison
Compare the approximated value with the calculator's value. Here's the provided data for reference:
- **using differentials**: [Student fills in this value]
- **using a calculator**: 3.0723 ✔
By conducting this exercise, you will better understand the accuracy of differential approximations and their practical use in calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6e1a3f1-b538-4464-8269-7761edea80d0%2Fada84935-612e-4523-9e17-4187652fae1e%2F2gg45a_processed.png&w=3840&q=75)
Transcribed Image Text:### Using Differentials to Approximate Values
In this exercise, we will use differentials to approximate the value of the given expression and then compare our estimate with the result obtained from a calculator. The goal is to round our answers to four decimal places for consistency and accuracy.
#### Given Expression
\( \sqrt{29} \)
#### Steps
1. **Approximation using Differentials**:
- We first approximate the value of the expression using differentials. This involves calculus techniques like linear approximation.
- Enter the result in the provided input box under the label "using differentials."
2. **Calculator Value**:
- Calculate the exact value using a calculator.
- For \( \sqrt{29} \), the calculator provides the value as 3.0723.
#### Comparison
Compare the approximated value with the calculator's value. Here's the provided data for reference:
- **using differentials**: [Student fills in this value]
- **using a calculator**: 3.0723 ✔
By conducting this exercise, you will better understand the accuracy of differential approximations and their practical use in calculus.
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