Standard Maclaurin seriesAQA A-Level Further Maths: Mind map

Exam questions on Standard Maclaurin series

1. Let $f(x)=\mathrm{e}^{3x}$.
   Use the first three terms of the series, with $x=0.1$, to estimate $\mathrm{e}^{0.3}$ to 3 decimal places.2 marks
2. Let $g(x)=\ln(1+2x)$.
   Use the series for $g(x)$, and for $g(-x)$, to find the first two non-zero terms in the series for $\ln\left(\dfrac{1+2x}{1-2x}\right)$.2 marks
3. Let $f(x)=\mathrm{e}^{x}\sin x$.
   Use standard series to find the expansion of $f(x)$ in ascending powers of $x$, up to and including the term in $x^3$.3 marks