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)

Related Topics

  • Mathematics

    Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

Related Documents

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

Citation

This page can be cited as

  • The Engineering ToolBox (2011). Taylor Series. [online] Available at: https://www.engineeringtoolbox.com/taylor-series-d_1750.html [Accessed Day Month Year].

Modify the access date according your visit.

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


















































12.6.9

.