Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Taylor Series

Function as an infinite sum of terms.

A Taylor serie is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. The generic expression:

f(x) = f(a) + f'(a) (x - a) / 1!  + f''(a) (x - a)2 / 2! + .....                           (1)

Examples

ex = 1 + x / 1! + x2 / 2! + x3 / 3! + ...                    (2)

ax = 1 + x ln(a) / 1! + (x ln(a))2 / 2!  + (x ln(a))3 / 3!  + ..                    (3)

ln(x) = 2( (x - 1) / (x + 1) + 1/3 ((x - 1) / (x + 1))3+ 1/5 ((x - 1) / (x + 1))5+ ..)                 (4)

ln(1 + x) = x - x2 / 2 + x3 / 3 - x4 / 4 + x5 / 5 + ...                      (5)

sin(x) = x - x3 / 3! + x5 / 5! - x7 / 7!+ ...                         (6)

cos(x) = 1 - x2 / 2! + x4 / 4! - x6 / 6!+ ...                       (7)

tan(x) = x + 1/3 x3  + 2 /15 x5 + 17 / 315 x7 + ...                       (8)

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


















































4.9.9

.