EXAMPLE 8 Working with the remainder In Example 4b of Section 11.2, we show that the nth-order Taylor polynomial for f(x) = In (1 – x) centered at 0 is п k P„(x) = -E x? x 3 п k=1 a. Find a bound on the error in approximating In (1 – x) by p;(x) for values of x in the interval [-.]. b. How many terms of the Taylor polynomial are needed to approximate values of f(x) = In (1 – x) with an error less than 10-³ on the interval [-}, 4]?
EXAMPLE 8 Working with the remainder In Example 4b of Section 11.2, we show that the nth-order Taylor polynomial for f(x) = In (1 – x) centered at 0 is п k P„(x) = -E x? x 3 п k=1 a. Find a bound on the error in approximating In (1 – x) by p;(x) for values of x in the interval [-.]. b. How many terms of the Taylor polynomial are needed to approximate values of f(x) = In (1 – x) with an error less than 10-³ on the interval [-}, 4]?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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![EXAMPLE 8 Working with the remainder In Example 4b of Section 11.2, we show
that the nth-order Taylor polynomial for f(x) = In (1 – x) centered at 0 is
п k
P„(x) = -E
x? x
3
п
k=1
a. Find a bound on the error in approximating In (1 – x) by p;(x) for values of x in the
interval [-.].
b. How many terms of the Taylor polynomial are needed to approximate values of
f(x) = In (1 – x) with an error less than 10-³ on the interval [-}, 4]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbad6e87c-b952-47be-97c1-fc98e6818b3d%2F1f3abcc0-b3e6-4c3a-8191-d628819a1325%2Fpngd09c.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 8 Working with the remainder In Example 4b of Section 11.2, we show
that the nth-order Taylor polynomial for f(x) = In (1 – x) centered at 0 is
п k
P„(x) = -E
x? x
3
п
k=1
a. Find a bound on the error in approximating In (1 – x) by p;(x) for values of x in the
interval [-.].
b. How many terms of the Taylor polynomial are needed to approximate values of
f(x) = In (1 – x) with an error less than 10-³ on the interval [-}, 4]?
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