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. (a) Find the Maclaurin series for 1 directly by computing the derivatives centered at x = 0. (1 – x)² (b) Now, find the Maclaurin series for 1 by treating the function as the derivative of another (1 – x)² function which you know the Maclaurin series for. Confirm that you get the same result. (c) Use the radius of convergence of the original series, the one you differentiated to find the series 1 to help you find the interval of convergence of the Maclaurin series for (1 for (1 – x)²'

. (a) Find the Maclaurin series for 1 directly by computing the derivatives centered at x = 0. (1 – x)² (b) Now, find the Maclaurin series for 1 by treating the function as the derivative of another (1 – x)² function which you know the Maclaurin series for. Confirm that you get the same result. (c) Use the radius of convergence of the original series, the one you differentiated to find the series 1 to help you find the interval of convergence of the Maclaurin series for (1 for (1 – x)²'

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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2. (a) Find the Maclaurin series for \(\frac{1}{(1-x)^2}\) directly by computing the derivatives centered at \(x = 0\). (b) Now, find the Maclaurin series for \(\frac{1}{(1-x)^2}\) by treating the function as the derivative of another function which you know the Maclaurin series for. Confirm that you get the same result. (c) Use the radius of convergence of the original series, the one you differentiated to find the series for \(\frac{1}{(1-x)^2}\), to help you find the interval of convergence of the Maclaurin series for \(\frac{1}{(1-x)^2}\).
Transcribed Image Text:2. (a) Find the Maclaurin series for \(\frac{1}{(1-x)^2}\) directly by computing the derivatives centered at \(x = 0\). (b) Now, find the Maclaurin series for \(\frac{1}{(1-x)^2}\) by treating the function as the derivative of another function which you know the Maclaurin series for. Confirm that you get the same result. (c) Use the radius of convergence of the original series, the one you differentiated to find the series for \(\frac{1}{(1-x)^2}\), to help you find the interval of convergence of the Maclaurin series for \(\frac{1}{(1-x)^2}\).
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