3. Find the Maclaurin series for ƒ(x) = ln(1+x) using the definition of a Maclaurin series. Also, find the associated radius of convergence. 4. Find the Taylor series for f(x) = ln(1 + x) centered at a = 3. Give the first 5 terms of the series expansion, and the general term, if possible. 5. Use a Maclaurin series for sin x to obtain the Maclaurin series for f(x) = sin(x¹).
3. Find the Maclaurin series for ƒ(x) = ln(1+x) using the definition of a Maclaurin series. Also, find the associated radius of convergence. 4. Find the Taylor series for f(x) = ln(1 + x) centered at a = 3. Give the first 5 terms of the series expansion, and the general term, if possible. 5. Use a Maclaurin series for sin x to obtain the Maclaurin series for f(x) = sin(x¹).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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