# TaylorPolynomial Command

##### Command Categories (All commands)

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 x2 at 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 a2 + 2a (x - a), the power series expansion of x2 at 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)2, the power series expansion with respect to x of x3 sin(y) at x = 3 to order 2.
• TaylorPolynomial(x^3 sin(y), y, 3, 2) gives x3 sin(3) + x3 cos(3) (y - 3) - x3 \mathrm{\mathsf{ \frac{sin(3) }{2} }} (y - 3)2, the power series expansion with respect to y of x3 sin(y) at y = 3 to order 2.
Note: The order has got to be an integer greater or equal to zero.
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