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a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. x² -0.12 Approximate e using f(x) = ex and p₂(x) = 1-x+ - 2 -0.12 ≈ ... a. Using the Taylor polynomial p2, e (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal places as needed.)

a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. x² -0.12 Approximate e using f(x) = ex and p₂(x) = 1-x+ - 2 -0.12 ≈ ... a. Using the Taylor polynomial p2, e (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal places as needed.)

Calculus: Early Transcendentals
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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**Taylor Polynomial Approximation** This exercise focuses on using a Taylor polynomial to approximate a given quantity and calculating the absolute error compared to an exact value. ### Instructions: **a.** Use the given Taylor polynomial \( p_2 \) to approximate the specified quantity. **b.** Compute the absolute error in the approximation, assuming the exact value is obtained using a calculator. --- ### Task Details: **Approximate \( e^{-0.12} \)** using: - Function: \( f(x) = e^{-x} \) - Taylor Polynomial: \( p_2(x) = 1 - x + \frac{x^2}{2} \) --- ### Steps to Follow: **a.** Using the Taylor polynomial \( p_2 \), approximate \( e^{-0.12} \approx \) [Enter Answer Here]. *Instructions*: Do not round off the numbers until the final calculation. Then, round your answer to four decimal places. **b.** Calculate the absolute error \(\approx\) [Enter Error Here]. *Instructions*: Use scientific notation, and include the multiplication symbol as necessary. Round your result to two decimal places.
Transcribed Image Text:**Taylor Polynomial Approximation** This exercise focuses on using a Taylor polynomial to approximate a given quantity and calculating the absolute error compared to an exact value. ### Instructions: **a.** Use the given Taylor polynomial \( p_2 \) to approximate the specified quantity. **b.** Compute the absolute error in the approximation, assuming the exact value is obtained using a calculator. --- ### Task Details: **Approximate \( e^{-0.12} \)** using: - Function: \( f(x) = e^{-x} \) - Taylor Polynomial: \( p_2(x) = 1 - x + \frac{x^2}{2} \) --- ### Steps to Follow: **a.** Using the Taylor polynomial \( p_2 \), approximate \( e^{-0.12} \approx \) [Enter Answer Here]. *Instructions*: Do not round off the numbers until the final calculation. Then, round your answer to four decimal places. **b.** Calculate the absolute error \(\approx\) [Enter Error Here]. *Instructions*: Use scientific notation, and include the multiplication symbol as necessary. Round your result to two decimal places.
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