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For the next three exercises, use power series operations to determine the Maclaurin series for the function. 2 1 2 x arctan (²) 3 In(1+x)-In(1-x) (1-x)³

For the next three exercises, use power series operations to determine the Maclaurin series for the function. 2 1 2 x arctan (²) 3 In(1+x)-In(1-x) (1-x)³

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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**Maclaurin Series Exercises** _For the next three exercises, use power series operations to determine the Maclaurin series for the function._ 1. \( \frac{2}{(1-x)^3} \) 2. \( x \arctan(x^2) \) 3. \( \ln(1+x) - \ln(1-x) \) _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 \( \cos(\sqrt{x}) + \ln(\cos x) \)._
Transcribed Image Text:**Maclaurin Series Exercises** _For the next three exercises, use power series operations to determine the Maclaurin series for the function._ 1. \( \frac{2}{(1-x)^3} \) 2. \( x \arctan(x^2) \) 3. \( \ln(1+x) - \ln(1-x) \) _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 \( \cos(\sqrt{x}) + \ln(\cos x) \)._
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