Taylor Series
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
Differential Calculus
Derivatives and differentiation expressions.
Fractions
Law of fractions
Hyperbolic Functions
Exponential functions related to the hyperbola.
Law of Sines
Calculate the angles in a generic triangle.
Polar vs. Cartesian Coordinates
Convert between Cartesian and Polar coordinates.
Scientific and Engineering Terms - ANSI Abbreviations
Abbreviations for Use on Drawings and in Text - ANSI Y1.1.
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions.
Vector Addition
Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more.