# What is the taylor series used for?

Apr 22, 2018

See the explanation below :-

#### Explanation:

Taylor series is used for the expansion of any continuously differentiable function in the term of a polynomial .

The formula for Taylor expansion is given below :-

For eg :

The Taylor series for ${e}^{x}$ is :

e^x = x^0/(0!) + x^1/(1!) + (x^2)/(2!) + (x^3)/(3!) + (x^4)/(4!) .................

:.e^x = 1 + x +(x^2)/(2!) + (x^3)/(3!) + (x^4)/(4!) .................

which is a polynomial of $x$.