Difference between revisions of "TaylorPolynomial Command"
From GeoGebra Manual
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; TaylorPolynomial[ <Function>, <x-Value>, <Order Number> ] | ; TaylorPolynomial[ <Function>, <x-Value>, <Order Number> ] | ||
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:*<code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)<sup>2</sup>'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''. | :*<code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)<sup>2</sup>'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''. | ||
− | :*<code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives '' | + | :*<code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''x<sup>3</sup> sin(3) + x<sup>3</sup> cos(3) (y - 3) - x<sup>3</sup> <math>\frac{sin(3) }{2}</math> (y - 3)<sup>2</sup>'', the power series expansion with respect to ''y'' of ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}} |
{{note| 1=The order has got to be an integer greater or equal to zero.}} | {{note| 1=The order has got to be an integer greater or equal to zero.}} |
Revision as of 14:29, 28 July 2015
- 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 \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.