TaylorPolynomial Command

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 sin(3) x³ + cos(3) x³ (y - 3) - \frac{sin(3) x³}{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.