Solved: Errors in approximations Carry out the procedure

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 80E Chapter 9.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 80E

Errors in approximations Carry out the procedure described in Exercise 77 with the following functions and approximations.

f(x) = ln(l + x).p1(x)= x,

Step-by-Step Solution:

Solution 80E

Step 1:

Calculating the errors using taylor polynomial ${p}_{1}(x)=x$ :

$Error=\left|{ln(0.8)-{p}_{1}(-0.2)}\right|\Rightarrow{}2.31\times{}1{0}^{-2}$
$Error=\left|{ln(0.9)-{p}_{1}(-0.1)}\right|\Rightarrow{}5.36\times{}1{0}^{-3}$
$Error=\left|{ln(1)-{p}_{1}(0.0)}\right|\Rightarrow{}0$
$Error=\left|{ln(1.1)-{p}_{1}(0.1)}\right|\Rightarrow{}4.68\times{}1{0}^{-3}$
$Error=\left|{ln(1.2)-{p}_{1}(0.2)}\right|\Rightarrow{}1.76\times{}1{0}^{-2}$

Calculating the errors using taylor polynomial ${p}_{2}(x)=x-\frac{{x}^{2}}{2}$ :

$Error=\left|{ln(0.8)-{p}_{2}(-0.2)}\right|\Rightarrow{}3.14\times{}1{0}^{-3}$
$Error=\left|{ln(0.9)-{p}_{2}(-0.1)}\right|\Rightarrow{}3.6\times{}1{0}^{-4}$
$Error=\left|{ln(1)-{p}_{2}(0.0)}\right|\Rightarrow{}0$
$Error=\left|{ln(1.1)-{p}_{2}(0.1)}\right|\Rightarrow{}3.1\times{}1{0}^{-4}$
$Error=\left|{ln(1.2)-{p}_{2}(0.2)}\right|\Rightarrow{}2.32\times{}1{0}^{-3}$

x	$Error=\left\|{ln(1+x)\ -{p}_{1}(x)}\right\|$	$Error=\left\|{ln(1+x)\ -{p}_{2}(x)}\right\|$
-0.2	$2.31\times{}1{0}^{-2}$	$3.14\times{}1{0}^{-3}$
-0.1	$5.36\times{}1{0}^{-3}$	$3.6\times{}1{0}^{-4}$
0.0	0	0
0.1	$4.68\times{}1{0}^{-3}$	$3.1\times{}1{0}^{-4}$
0.2	$1.76\times{}1{0}^{-2}$	$2.32\times{}1{0}^{-3}$

Step 2 of 2

Chapter 9.1, Problem 80E is Solved

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 80E from chapter: 9.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: approximations, errors, described, carry, exercise. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. Since the solution to 80E from 9.1 chapter was answered, more than 357 students have viewed the full step-by-step answer. The answer to “Errors in approximations Carry out the procedure described in Exercise 77 with the following functions and approximations.f(x) = ln(l + x).p1(x)= x,” is broken down into a number of easy to follow steps, and 22 words.