Find number of terms in taylor expansion upto when error is 10^(-6)

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khadija raza
khadija raza 2018-7-19
评论： Walter Roberson 2018-7-22
Find number of terms in taylor expansion upto when error is 10^(-6)
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khadija raza
khadija raza 2018-7-22
what about error sir Walter? we have to consider the error to find number of terms
Walter Roberson
Walter Roberson 2018-7-22
The number of terms is going to be quite different for n around 5 than it is for n around 555555555555555555555555555 . The magnitude of n matters because your error requirement is stated in absolute form, not in relative form.
I suspect the taylor series is only valid for continuous functions, but if you do not restrict n to integer then you can get large complex magnitudes.
As you have not stated an expansion point, it would make more sense to use a series expansion instead of a taylor expansion, or at least a Maclaurin series (taylor around 0)

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Aquatris
Aquatris 2018-7-19
There is an approximation for upper bound on the error (or remaining terms in Taylor expansion). Here is a link that explains the method. From there, it is still not a closed form solution but you can roughly guess the order you want for desired error.

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