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#### power series development

Hallo

I have got a mathematical problem.
I want to approximate an exponential function with a taylor polynom.

1+x+x^2/2+x^3/6+...+x^n/n!+....

Depending on the intervall of my value x i need to have a certain amount of polynoms for my approximation. I have found a table with a degree of polynoms that correspond with a specific intervall of x. With this table it is possible to obtain an exponential approximation of 10 digits behind the komma....

x degree of Polynom
0.05 5
0.1 6
0.2 8
0.5 10
1 13
2 17
5 25
10 36

The question i have is not mathematically easy to solve.
Can somebody show me the mathematical derivation of this table ?

Thank you !!!
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epl
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i would imagine the table was derived by calculating terms of the taylor series / maclaurin series until the (total of the outstanding) terms become insignificant.

on the other hand there may be a direct calculation of the remainder series (ie the terms from n+1 to infinity) that if you need a proper mathematical derivation.

for what it's worth i make the last two 28 and 43 in excel (not 25 and 36)

edit:- i think your table is accurate to ten significant digits rather than ten digits after the comma as you say.
Last edited by epl; August 22nd, 2003 at 03:28 PM.