# Maclaurin and Taylor series – Edexcel FP2

#### 6. Maclaurin and Taylor series – Edexcel Further Pure Mathematics 2 (FP2)

What students need to learn:
Third and higher order derivatives.

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

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

Use of Taylor series method for series solutions of differential equations.
Students may, for example, be required to find the solution in powers of $$x$$ as far as the term in $$x^4$$ , of the differential equation
$$\dfrac{d^2y}{dx^2} + x \dfrac{dy}{dx} + y = 0$$ ,
such that $$y = 1$$, $$\dfrac{dy}{d x} = 0$$ at $$x = 0$$.