Maclaurin seriesEdexcel International A Level Further Maths: Mind map

Exam questions on Maclaurin series

1. A function is defined by $f(x)=\mathrm{e}^{3x}$.
   Write down the Maclaurin series of $f(x)$ up to and including the term in $x^3$, and use it with $x=0.3$ to estimate $\mathrm{e}^{0.9}$ to 3 significant figures.2 marks
2. A function is defined by $f(x)=\cos2x$.
   Use the identity $\cos2x=1-2\sin^2x$ and the Maclaurin series of $\cos2x$ up to the term in $x^4$ to find the first two non-zero terms of the Maclaurin series of $\sin^2x$.2 marks
3. A function is defined by $f(x)=\ln(1+x)$, for $-1<x\le1$.
   Use differentiation to find the Maclaurin series of $f(x)$ up to and including the term in $x^3$.3 marks