(a) Verify thatd/ dx (x sin(x3)) = sin(x3) + 3x3 cos(x3). (b) Use multiplication and/or substitution in the Maclaurin series for the sine and the cosine to find the Maclaurin series for x sin(x3), sin(x3), and 3x3 cos(x3).(c) Use Theorem 8.11 to find the Maclaurin series for d/ dx (x sin(x 3)), and show that this series is the sum of the Maclaurin series for sin(x 3) and 3x3 cos(x3) you obtained in part (b).
(a) Verify thatd/ dx (x sin(x3)) = sin(x3) + 3x3 cos(x3). (b) Use multiplication and/or substitution in the Maclaurin series for the sine and the cosine to find the Maclaurin series for x sin(x3), sin(x3), and 3x3 cos(x3).(c) Use Theorem 8.11 to find the Maclaurin series for d/ dx (x sin(x 3)), and show that this series is the sum of the Maclaurin series for sin(x 3) and 3x3 cos(x3) you obtained in part (b).
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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(a) Verify that
d/ dx (x sin(x3)) = sin(x3) + 3x3 cos(x3).
(b) Use multiplication and/or substitution in the Maclaurin series for the sine and the cosine to find the Maclaurin series for x sin(x3), sin(x3), and 3x3 cos(x3).
(c) Use Theorem 8.11 to find the Maclaurin series for d/ dx (x sin(x 3)), and show that this series is the sum of the Maclaurin series for sin(x 3) and 3x3 cos(x3) you obtained in part (b).
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