12 . The function f is given by f x
2
( ) ln ( x 1 ) � � .
( a ) ( i ) Find the first three derivatives of f( x ).
It is also given that f
( 4 )
( x) ��
4 2
12 ( x �6x �1 )
( x �1 )
2 4
.
( ii ) Using the above results to find the Maclaurin series for f( x ) up to and including the
4 x term .
2 sin x
( b ) Find the Maclaurin series for ln �( 1 ) � term . x � up to and including the
2 sin y
The region R is enclosed by the graph of g( y) y ln �( y 1 ) � and the lines y � 0.7 and y � 1.3 .
[ 10 ]
5 x
� � , the y -axis
[ 5 ]
( c ) Using ( b ) to find the volume of the solid of revolution formed when R is rotated through 2π about the y -axis .
[ 4 ]
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