Difference between revisions of "TaylorPolynomial Command"
From GeoGebra Manual
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Revision as of 13:40, 10 September 2011
- TaylorPolynomial[ <Function>, <Number a>, <Number n>]
- Creates the power series expansion for the given function about the point x = a to order n.
- Example:
TaylorPolynomial[x^2, 3, 1]gives 6 x - 9, the power series expansion of x2 at x = 3 to order 1.
CAS Syntax
- TaylorPolynomial[ <Function>, <Number a>, <Number n>]
- Creates the power series expansion for the given function about the point x = a to order n.
- Example:
TaylorPolynomial[x^2, a, 1]gives -a2 + 2 a x, the power series expansion of x2 at x = a to order 1.
- TaylorPolynomial[ <Function>, <Variable>, <Number a>, <Number n>]
- Creates the power series expansion for the given function with respect to the given variable about the point Variable = a to order n.
- Example:
TaylorPolynomial[x^3 sin(y), x, 3, 2]gives sin(y) (9 x2 - 27 x + 27), the power series expansion with respect to x of x3 sin(y) at x = 3 to order 2.
- Example:
TaylorPolynomial[x^3 sin(y), y, 3, 2]gives \frac{cos(3) x^{3} (2 y - 6) + sin(3) x^{3} (-y^{2} + 6 y - 7)}{2} , the power series expansion with respect to y of x3 sin(y) at y = 3 to order 2.
Note: The order n has got to be an integer greater or equal to zero.
