Difference between revisions of "TaylorPolynomial Command"
From GeoGebra Manual
m (Bot: Automated text replacement (-{{command +{{command|cas=true)) |
m (Text replace - "<div class="box info"> 48px|left This page is part of the official manual for print and pdf. For structural reasons normal users can't edit this page. If you found any errors on this page please contact ) |
||
| Line 1: | Line 1: | ||
| − | <noinclude>{{Manual Page|version=4. | + | <noinclude>{{Manual Page|version=4.2}}</noinclude> |
{{command|cas=true|function}} | {{command|cas=true|function}} | ||
; TaylorPolynomial[ <Function>, <Number a>, <Number n>] | ; TaylorPolynomial[ <Function>, <Number a>, <Number n>] | ||
Revision as of 22:30, 9 March 2013
- 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.
