FP2.6 - Maclaurin and Taylor series

Third and higher order derivatives.

Use fp2.6.1 - third and higher order derivatives to connect the rule to the data and decision in the question.

This matters because fp2.6.1 - third and higher order derivatives determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.6.1 - third and higher order derivatives to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.6.1 - Third and higher order derivatives is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Derivation and use of Maclaurin The derivation of the series expansion of ex, sin x, cos x, series. ln (1 + x) and other simple functions may be required.

Use fp2.6.2 - derivation to connect the rule to the data and decision in the question.

This matters because fp2.6.2 - derivation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.6.2 - derivation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.6.2 - Derivation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Derivation and use of Taylor series.; The derivation, for example, of the expansion of sin x in ascending powers of (x − π) up to and including the term in (x − π)3.

Use fp2.6.3 - derivation to connect the rule to the data and decision in the question.

This matters because fp2.6.3 - derivation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.6.3 - derivation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP2.6.3 - Derivation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use of Taylor series method for Students may, for example, be required to find the solution series solutions of differential in powers of x as far as the term in x4,of the differential equations. equation d2y dy dy + x + y = 0, such that y = 1, = 0 at x = 0. dx2 dx dx.

Use fp2.6.4 - taylor series method for differential equations to connect the rule to the data and decision in the question.

This matters because fp2.6.4 - taylor series method for differential equations determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp2.6.4 - taylor series method for differential equations to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.