Maclaurin seriesEdexcel A-Level Further Maths: Mind map

Exam questions on Maclaurin series

1. The function $\mathrm{f}(x)=\mathrm{e}^{2x}$ is expanded as a Maclaurin series.
   Use the first four terms of the series with $x=0.05$ to estimate the value of $\mathrm{e}^{0.1}$, giving your answer to 5 decimal places.2 marks
2. Let $\mathrm{g}(x)=\ln(1+3x)$.
   Find the first three non-zero terms of the Maclaurin series of $\mathrm{g}(x)$.2 marks
3. Let $\mathrm{f}(x)=\mathrm{e}^x\sin x$.
   Use the standard series for $\mathrm{e}^x$ and $\sin x$ to find the series expansion of $\mathrm{f}(x)$ up to and including the term in $x^3$.3 marks