Maclaurin seriesEdexcel A-Level Further Maths: Flashcards

What these 12 flashcards ask

Maclaurin series of f(x)?
Series for e^x and its validity?
Series for \sin x and its validity?
Series for \cos x and its validity?
Series for \ln(1+x) and its validity?
Series for (1+x)^n and its validity?
General term of e^{2x}?
General term of \ln(1+x)?
Validity of the series for \ln(1+3x)?
First terms of e^x\sin x?
First terms of \tan x?
First terms of \ln\frac{1+x}{1-x}?

Exam questions on Maclaurin series

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
Let $\mathrm{g}(x)=\ln(1+3x)$ .
Find the first three non-zero terms of the Maclaurin series of $\mathrm{g}(x)$ .2 marks
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).