a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. approximation-exact |exact c. Compute the percent error in the approximation, 100 • where the exact value is given by a calculator. f(x) = x+2 a=0; ,2 a. L(x) = || b. Using the linear approximation, 22 2.2 (Round to three decimal places as needed.) C. The percent error in the approximation is %. (Round to three decimal places as needed.)
a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. approximation-exact |exact c. Compute the percent error in the approximation, 100 • where the exact value is given by a calculator. f(x) = x+2 a=0; ,2 a. L(x) = || b. Using the linear approximation, 22 2.2 (Round to three decimal places as needed.) C. The percent error in the approximation is %. (Round to three decimal places as needed.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Linear Approximation and Percent Error Calculation
#### Problem Statement
1. **Linear Approximation Setup:**
- Write the equation of the line that represents the linear approximation to the following function at the given point \( a \).
- Use the linear approximation to estimate the given quantity.
2. **Percent Error Calculation:**
- Compute the percent error in the approximation using the formula:
\[
100 \cdot \frac{\text{approximation} - \text{exact}}{\text{exact}}
\]
where the exact value is given by a calculator.
#### Given Data
- Function: \( f(x) = \frac{1}{x+2} \)
- Point of approximation: \( a = 0 \)
- Exact value: \( \frac{1}{2.2} \)
### Step-by-Step Solution
#### a. Write the Linear Approximation Equation
Determine the linear approximation \( L(x) \):
\[ L(x) = \]
#### b. Estimation Using Linear Approximation
Estimate \( \frac{1}{2.2} \) using the linear approximation:
\[ \frac{1}{2.2} \approx \]
(Round to three decimal places as needed.)
#### c. Compute Percent Error
Calculate the percent error in the approximation:
\[ \text{The percent error in the approximation is} \, \, \%\]
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff0dd34-3494-48ea-8c6c-10579239d5c2%2F8284506b-f24c-4f27-8af1-ee0a1260dce8%2F5bxmdo2j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Approximation and Percent Error Calculation
#### Problem Statement
1. **Linear Approximation Setup:**
- Write the equation of the line that represents the linear approximation to the following function at the given point \( a \).
- Use the linear approximation to estimate the given quantity.
2. **Percent Error Calculation:**
- Compute the percent error in the approximation using the formula:
\[
100 \cdot \frac{\text{approximation} - \text{exact}}{\text{exact}}
\]
where the exact value is given by a calculator.
#### Given Data
- Function: \( f(x) = \frac{1}{x+2} \)
- Point of approximation: \( a = 0 \)
- Exact value: \( \frac{1}{2.2} \)
### Step-by-Step Solution
#### a. Write the Linear Approximation Equation
Determine the linear approximation \( L(x) \):
\[ L(x) = \]
#### b. Estimation Using Linear Approximation
Estimate \( \frac{1}{2.2} \) using the linear approximation:
\[ \frac{1}{2.2} \approx \]
(Round to three decimal places as needed.)
#### c. Compute Percent Error
Calculate the percent error in the approximation:
\[ \text{The percent error in the approximation is} \, \, \%\]
(Round to three decimal places as needed.)
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