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1. (25%) Consider the function f(x) = (x + 2)4. 1a. (7.5%) Use a 2nd-order Maclaurin series expansion to approximate the value of ƒ (5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1b. (10%) Use a 4th-order Maclaurin series expansion to approximate the value of f(5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1c. (2.5%) Calculate the absolute approximate percentage error (εa) between the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answer. 1d. (5%) Calculate the absolute true percentage errors (εt) of the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answers.

1. (25%) Consider the function f(x) = (x + 2)4. 1a. (7.5%) Use a 2nd-order Maclaurin series expansion to approximate the value of ƒ (5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1b. (10%) Use a 4th-order Maclaurin series expansion to approximate the value of f(5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1c. (2.5%) Calculate the absolute approximate percentage error (εa) between the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answer. 1d. (5%) Calculate the absolute true percentage errors (εt) of the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answers.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1. (25%) Consider the function f(x) = (x + 2)4. 1a. (7.5%) Use a 2nd-order Maclaurin series expansion to approximate the value of ƒ (5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1b. (10%) Use a 4th-order Maclaurin series expansion to approximate the value of f(5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1c. (2.5%) Calculate the absolute approximate percentage error (εa) between the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answer. 1d. (5%) Calculate the absolute true percentage errors (εt) of the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answers.
Transcribed Image Text:1. (25%) Consider the function f(x) = (x + 2)4. 1a. (7.5%) Use a 2nd-order Maclaurin series expansion to approximate the value of ƒ (5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1b. (10%) Use a 4th-order Maclaurin series expansion to approximate the value of f(5). Use 4 significant digits and rounding in your intermediate calculations and when reporting your final answer. 1c. (2.5%) Calculate the absolute approximate percentage error (εa) between the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answer. 1d. (5%) Calculate the absolute true percentage errors (εt) of the estimates obtained in problems 1a and 1b. Use 4 significant digits and rounding in your intermediate calculations and final answers.
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