Maclaurin series of a functionAQA A-Level Further Maths: Mind map

Exam questions on Maclaurin series of a function

1. Let $f(x)=\ln(\cos x)$ for $-\frac{\pi}{2}<x<\frac{\pi}{2}$.
   Given that $f'''(0)=0$ and $f^{(4)}(0)=-2$, find the first two non-zero terms of the Maclaurin series of $f(x)$.2 marks
2. Let $f(x)=\dfrac{1}{1-2x}$.
   Deduce an expression for $f^{(r)}(0)$ in terms of $r$.2 marks
3. Let $f(x)=\tan x$.
   Show that $f'''(0)=2$.3 marks