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an error of magnitude less than 1-cos(2x) 4 Use the identity sin² a to obtain the Maclaurin series for sin² x. Then differentiate this series to 2 obtain the Maclaurin series for 2 sin x cosx. 5 Use the Taylor series definition (determine the pattern for all derivatives, etc.) to obtain the Maclaurin series for sin(2x) and verify that this is the same as the series for 2 sin a cos z from the previous exercise.

an error of magnitude less than 1-cos(2x) 4 Use the identity sin² a to obtain the Maclaurin series for sin² x. Then differentiate this series to 2 obtain the Maclaurin series for 2 sin x cosx. 5 Use the Taylor series definition (determine the pattern for all derivatives, etc.) to obtain the Maclaurin series for sin(2x) and verify that this is the same as the series for 2 sin a cos z from the previous exercise.

Algebra & Trigonometry with Analytic Geometry
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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Can someone show all the steps for solving problem 5?

1 Estimate the error if P3(x) = x - x³/6 is used to approximate the value of sin x at x = 0.1. 2 If cos z is replaced by 1-²/2 and 2x < 0.5, what estimate can be made of the error? Does 1-2²/2 tend to be too large, or too small? 3 How many terms of the Maclaurin series for In(1+x) should you add up to be sure of calculating In(1.1) with an error of magnitude less than 10-8? 4 Use the identity sin²x = 1-cos(2x) to obtain the Maclaurin series for sin²x. Then differentiate this series to 2 obtain the Maclaurin series for 2 sin x cos x. 5 Use the Taylor series definition (determine the pattern for all derivatives, etc.) to obtain the Maclaurin series for sin(2x) and verify that this is the same as the series for 2 sin cos x from the previous exercise.
Transcribed Image Text:1 Estimate the error if P3(x) = x - x³/6 is used to approximate the value of sin x at x = 0.1. 2 If cos z is replaced by 1-²/2 and 2x < 0.5, what estimate can be made of the error? Does 1-2²/2 tend to be too large, or too small? 3 How many terms of the Maclaurin series for In(1+x) should you add up to be sure of calculating In(1.1) with an error of magnitude less than 10-8? 4 Use the identity sin²x = 1-cos(2x) to obtain the Maclaurin series for sin²x. Then differentiate this series to 2 obtain the Maclaurin series for 2 sin x cos x. 5 Use the Taylor series definition (determine the pattern for all derivatives, etc.) to obtain the Maclaurin series for sin(2x) and verify that this is the same as the series for 2 sin cos x from the previous exercise.
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