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For the next three exercises, use power series operations to determine the Maclaurin series for the function. 1 2 (1-x)³ 2 x arctan(x²) 3 In(1+x)-In(1-x) 4 Determine the first three non-zero terms in the Maclaurin series for esinz 5 Determine the first three non-zero terms in the Maclaurin series for cos(√) + In(cos x).

For the next three exercises, use power series operations to determine the Maclaurin series for the function. 1 2 (1-x)³ 2 x arctan(x²) 3 In(1+x)-In(1-x) 4 Determine the first three non-zero terms in the Maclaurin series for esinz 5 Determine the first three non-zero terms in the Maclaurin series for cos(√) + In(cos x).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 71E
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### Power Series and Maclaurin Series Exercises For the next three exercises, use power series operations to determine the Maclaurin series for the function. 1. Evaluate the Maclaurin series for the function \(\frac{2}{(1-x)^3}\). 2. Evaluate the Maclaurin series for the function \(x \arctan(x^2)\). 3. Evaluate the Maclaurin series for the function \(\ln(1+x) - \ln(1-x)\). --- ### Additional Maclaurin Series Exercises 4. **Determine the first three non-zero terms in the Maclaurin series for \(e^{\sin x}\).** 5. **Determine the first three non-zero terms in the Maclaurin series for \(\cos(\sqrt{x}) + \ln(\cos x)\).** These exercises are designed to help you practice using power series operations to find the Maclaurin series for various functions.
Transcribed Image Text:### Power Series and Maclaurin Series Exercises For the next three exercises, use power series operations to determine the Maclaurin series for the function. 1. Evaluate the Maclaurin series for the function \(\frac{2}{(1-x)^3}\). 2. Evaluate the Maclaurin series for the function \(x \arctan(x^2)\). 3. Evaluate the Maclaurin series for the function \(\ln(1+x) - \ln(1-x)\). --- ### Additional Maclaurin Series Exercises 4. **Determine the first three non-zero terms in the Maclaurin series for \(e^{\sin x}\).** 5. **Determine the first three non-zero terms in the Maclaurin series for \(\cos(\sqrt{x}) + \ln(\cos x)\).** These exercises are designed to help you practice using power series operations to find the Maclaurin series for various functions.
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