8. Use the 3rd degree Taylor polynomial centered at x = 0 for f(x) = e to estimate e and determine the maximum error.

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Chapter1: Functions And Models
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8. Use the 3rd degree Taylor polynomial centered at x = 0 for f(x)= e² to estimate e and
determine the maximum error.
9. The Maclaurin series for arctans converges for -1 SS1 and is given by
(-1) 22²-1).
arctanr=
Since tan()= 1, it follows that the series for 7 is = 4 arctan 1.
(a) Determine the number of terms the series that need to be summed in order to
ensure that
|4arctan 1 – #| < 107,
-
(b) How many terms are required to ensure the 10-10 accuracy needed for an approxi-
mation to ?
Transcribed Image Text:8. Use the 3rd degree Taylor polynomial centered at x = 0 for f(x)= e² to estimate e and determine the maximum error. 9. The Maclaurin series for arctans converges for -1 SS1 and is given by (-1) 22²-1). arctanr= Since tan()= 1, it follows that the series for 7 is = 4 arctan 1. (a) Determine the number of terms the series that need to be summed in order to ensure that |4arctan 1 – #| < 107, - (b) How many terms are required to ensure the 10-10 accuracy needed for an approxi- mation to ?
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