Question 0814

Maclaurin Series

2014 Paper 1 Question 8 Variant

Question

It is given that

f(x) = \frac{1}{64+x^2},

where

{x \in \mathbb{R}.}

(i)

Write down

\int f(x) \; \mathrm{d}x.

[1]

(ii)

Find the binomial expansion for

{f(x),}

up to and including the term in

{x^6.}

Give the coefficients as exact fractions in their simplest form.

[4]

(iii)

Hence, or otherwise, find the first four non-zero terms of the Maclaurin series for

{\tan^{-1} (\frac{1}{8} x).}

Give the coefficients as exact fractions in their simplest form.

[4]