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Suppose you decide to build a calculator that will compute values of \( e^{x} \). Having l ...
Suppose you decide to build a calculator that will compute values of \( e^{x} \). 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 \( e^{x} \) whenever \( -1 \leq x \leq 1 \), 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 \( e^{x} \) whenever \( -2 \leq x \leq 2 \) ? C. The following thought occurs to you: To compute a value \( e^{N} \), 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.