# TaylorPolynomial Command

From GeoGebra Manual

- TaylorPolynomial( <Function>, <x-Value>, <Order Number> )
- Creates the power series expansion for the given function at the point
*x-Value*to the given order. **Example:**`TaylorPolynomial(x^2, 3, 1)`

gives*9 + 6 (x - 3)*, the power series expansion of*x*at^{2}*x = 3*to order*1*.

## CAS Syntax

- TaylorPolynomial( <Expression>, <x-Value>, <Order Number> )
- Creates the power series expansion for the given expression at the point
*x-Value*to the given order. **Example:**`TaylorPolynomial(x^2, a, 1)`

gives*a*, the power series expansion of^{2}+ 2a (x - a)*x*at^{2}*x = a*to order*1*.

- TaylorPolynomial( <Expression>, <Variable>, <Variable Value>, <Order Number> )
- Creates the power series expansion for the given expression with respect to the given variable at the point
*Variable Value*to the given order. **Examples:**`TaylorPolynomial(x^3 sin(y), x, 3, 2)`

gives*27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)*, the power series expansion with respect to^{2}*x*of*x*at^{3}sin(y)*x = 3*to order*2*.`TaylorPolynomial(x^3 sin(y), y, 3, 2)`

gives*x*, the power series expansion with respect to^{3}sin(3) + x^{3}cos(3) (y - 3) - x^{3}\frac{sin(3) }{2} (y - 3)^{2}*y*of*x*at^{3}sin(y)*y = 3*to order*2*.

**Note:**The order has got to be an integer greater or equal to zero.