7/28/2019 Unsolved Problems Maclaurin's

1/1

1

Expand the following functions into a series with a minimum of three nonzero terms :

(1) tan12

3

313

x

xx (2) sin1 21 2 xx

(3) cos11

1

xx

xx

(4) tan1pxq

qxp

(5) cot1

x

x

1

1

Expand the following functions into a series

(i) sec12

21

1

x

(ii) sec112

1

2 x (iii) tan1 21 xx

(iv) sin1 (3x4x3) (v) cos1 (3x 4x3)

Find the series expansions of the following functions :

(i) sinh1 (3x+ 4x3) (ii) cot1x

x

1

1

(iii) tan1x

x

1

1(iv) cot1

x

x2

1