2. After losing your internet connection and your phone (it's been one of those days), you decide to build a calculator that will compute values of e". Having learned about Taylor series, and remembering that computers are good at addition and multiplication, you decide to use a Taylor polynomial to do the job. The display of your calculator will show six digits after the decimal point. A. If you would like your calculator to display accurate values of e" whenever -1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Can you help me solve A,B,& C. 

2. After losing your internet connection and your phone (it's been one of those days), you decide to build a calculator
that will compute values of e". Having learned about Taylor series, and remembering that computers are good at
addition and multiplication, you decide to use a Taylor polynomial to do the job. The display of your calculator will
show six digits after the decimal point.
A. If you would like your calculator to display accurate values of e whenever -1 <x < 1, then what is the
lowest-degree Taylor polynomial you can use?
B. What is the lowest-degree Taylor polynomial you can use if you would like your calculator to display accurate
values of e whenever -2 < x < 2?
C. The following thought occurs to you: To compute a value e, where N is some large number, why not program
your calculator to use a Taylor polynomial centered at a number that is close to N? Is this a practical strategy?
Explain.
Transcribed Image Text:2. After losing your internet connection and your phone (it's been one of those days), you decide to build a calculator that will compute values of e". Having learned about Taylor series, and remembering that computers are good at addition and multiplication, you decide to use a Taylor polynomial to do the job. The display of your calculator will show six digits after the decimal point. A. If you would like your calculator to display accurate values of e whenever -1 <x < 1, then what is the lowest-degree Taylor polynomial you can use? B. What is the lowest-degree Taylor polynomial you can use if you would like your calculator to display accurate values of e whenever -2 < x < 2? C. The following thought occurs to you: To compute a value e, where N is some large number, why not program your calculator to use a Taylor polynomial centered at a number that is close to N? Is this a practical strategy? Explain.
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