TaylorPolynomial Command
- TaylorPolynomial( <Function>, <x-Value>, <Order Number> )
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Creates the Taylor series expansion of the given function at the point x-Value up to the given order.
TaylorPolynomial(x^2, 3, 1) gives 9 + 6 (x - 3), the Taylor series expansion of x2 at x = 3 up to order 1.
CAS Syntax
- TaylorPolynomial( <Expression>, <x-Value>, <Order Number> )
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Creates the Taylor series expansion of the given expression at the point x-Value up to the given order.
TaylorPolynomial(x^2, a, 1) gives a2 + 2a (x - a), the Taylor series expansion of x2 at x = a up to order
1.
- TaylorPolynomial( <Expression>, <Variable>, <Variable Value>, <Order Number> )
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Creates the Taylor series expansion of the given expression with respect to the given variable at the point Variable Value up to the given order.
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TaylorPolynomial(x^3 sin(y), x, 3, 2)gives 27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)2, the Taylor series expansion with respect to x of x3 sin(y) at x = 3 up 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 Taylor series expansion with respect to y of x3 sin(y) at y = 3 up to order 2.
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The order has got to be an integer greater or equal to zero. |