Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal notation. Give your answer to four decimal places.) f(3.1, 8.8) - help (fractions) The
Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal notation. Give your answer to four decimal places.) f(3.1, 8.8) - help (fractions) The
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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![**Exercise: Linear Approximation**
**Objective:**
Use the linear approximation to \( f(x, y) = \frac{12x^2}{y^2 + 7} \) at the point \((3, 9)\) to estimate the value of \( f(3.1, 8.8) \).
**Instructions:**
1. Use decimal notation.
2. Provide your answer to four decimal places.
**Tasks:**
1. Calculate the approximation for \( f(3.1, 8.8) \).
\[
f(3.1, 8.8) \approx \quad \underline{\phantom{answer}}
\]
(Click on "help (fractions)" if you need assistance.)
2. Determine the percentage error of your approximation.
\[
\text{The percentage error is} \quad \underline{\phantom{answer}} \%
\]
**Note:**
- Ensure precision in your calculations.
- Refer to the help section if you have questions about using fractions or decimal conversion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ced33f3-9784-42db-addd-1c9bdb632f18%2Fff60855a-3e54-4b31-97aa-c910d34656f4%2F5qig52_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise: Linear Approximation**
**Objective:**
Use the linear approximation to \( f(x, y) = \frac{12x^2}{y^2 + 7} \) at the point \((3, 9)\) to estimate the value of \( f(3.1, 8.8) \).
**Instructions:**
1. Use decimal notation.
2. Provide your answer to four decimal places.
**Tasks:**
1. Calculate the approximation for \( f(3.1, 8.8) \).
\[
f(3.1, 8.8) \approx \quad \underline{\phantom{answer}}
\]
(Click on "help (fractions)" if you need assistance.)
2. Determine the percentage error of your approximation.
\[
\text{The percentage error is} \quad \underline{\phantom{answer}} \%
\]
**Note:**
- Ensure precision in your calculations.
- Refer to the help section if you have questions about using fractions or decimal conversion.
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