Question 0820

Maclaurin Series

2020 Paper 1 Question 3 Variant

Question

It is given that

{f(x) = \ln( 1 + \sin 6 x ).}

(i)

Show that

f''(x) = \frac{k}{1+\sin 6 x},

where

{k}

is a constant to be found.

[3]

(ii)

Hence find the first three non-zero terms of the Maclaurin expansion of

{f(x).}

[4]