Difference between revisions of "TaylorPolynomial Command"
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| − | ; TaylorPolynomial[Function, Number a, Number n]: Creates the power series expansion for the given function about the point ''x = a'' to order ''n''. | + | ; TaylorPolynomial[ <Function>, <Number a>, <Number n>] |
| + | :Creates the power series expansion for the given function about the point ''x = a'' to order ''n''. | ||
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''6 x - 9'', the power series expansion of ''x<sup>2</sup>'' at ''x = 3'' to order ''1''.</div>}} | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''6 x - 9'', the power series expansion of ''x<sup>2</sup>'' at ''x = 3'' to order ''1''.</div>}} | ||
| − | |||
==CAS Syntax== | ==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''. | + | ; TaylorPolynomial[ <Function>, <Number a>, <Number n>] |
| + | :Creates the power series expansion for the given function about the point ''x = a'' to order ''n''. | ||
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives ''-a<sup>2</sup> + 2 a x'', the power series expansion of ''x<sup>2</sup>'' at ''x = a'' to order ''1''.</div>}} | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives ''-a<sup>2</sup> + 2 a x'', the power series expansion of ''x<sup>2</sup>'' at ''x = a'' to order ''1''.</div>}} | ||
| − | ; 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''. | + | ;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| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''sin(y) (9 x<sup>2</sup> - 27 x + 27)'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''.</div>}} | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''sin(y) (9 x<sup>2</sup> - 27 x + 27)'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''.</div>}} | ||
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''<math>x³\frac{(-y² sin(3) + y (2cos(3) + 6sin(3)) - 6cos(3) - 7sin(3))}{2}</math>'' , the power series expansion with respect to ''y'' of ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}} | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''<math>x³\frac{(-y² sin(3) + y (2cos(3) + 6sin(3)) - 6cos(3) - 7sin(3))}{2}</math>'' , the power series expansion with respect to ''y'' of ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}} | ||
| − | {{note| The order n has got to be an integer greater or equal to zero.}} | + | {{note| 1=The order n has got to be an integer greater or equal to zero.}} |
Revision as of 14:15, 5 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 x³\frac{(-y² sin(3) + y (2cos(3) + 6sin(3)) - 6cos(3) - 7sin(3))}{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.
