# Online Taylor Series Calculator



An online taylor series calculator is presented.

## Definition of Taylor Series

For a function $f$ whose derivatives are defined in an interval containing $a$, The Taylor series of function $f$ at $x = a$ is given by $\sum_{k=0}^{\infty} \dfrac{f^k(a)}{k!} (x-a)^k = f(a) + f'(a) (x-a) + \dfrac{f''(a)}{2!} (x-a)^2 + ... + \dfrac{f^{(n)}(a)}{n!} (x-a)^n + ...$
In practice a Taylor polynomial $P_n(x)$ is obtained by truncating Taylor series to $n$ terms.
The online calculator presented below, finds the Taylor polynomial at $x = a$ including $n$ terms.

## Use of Taylor Series Calculator

1 - Enter and edit function $f(x)$ and click "Enter Function" then check what you have entered.
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x*log(x)).(more notes on editing functions are located below)
2 - Click "Calculate Taylor Expansion" to obain the Taylor expansion of the entered function at the values of $a$ and $n$ entered.
Note that $a$ can take integer values only and $n$ is a positive integer.

$f(x)$ =

n =       a =

Notes: In editing functions, use the following:
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x*ln(x+1))
2 - The function square root function is written as (sqrt). (example: sqrt(x^2+1)
Here are some examples of functions that you may copy and paste to practice:
e^x     ln(x^2+1)       e^(-x^2)       1/(x-2)       sin(2*x - 2)      sqrt(x^2+1)