Analysis and Approaches for IBDP Maths Ebook 2 | Page 208

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
2 3
x x (3)
f ( x) � f (0) � xf �(0) � f ��(0) � f (0) �
2! 3!
2 3
3 x 9 x 27
f ( x) � 0 � x � �� � � � � � � � � � � � �
� � M1
� 2 � 2 � 4 � 6 � 4 �
3 9 2 9 3
f ( x)
� � x � x � x � A1
2 8 8
2
2�
3x � 6
1
2�3x
�
3
5
3x ��
3
5
x �� (A1) for correct value
9
2 3
3 � 5 � 9 � 5 � 9 � 5 �
�ln 6 � � �� � � �� � � ��
�
2 � 9 � 8 � 9 � 8 � 9 �
M1
445
ln 6 �
324
A1
[6]
[3]
Exercise 64
1. (a) By successive differentiation, find the Maclaurin series of
(b)
far as the term in
3
x .
Hence, use this series to find an approximate value of
0.03
e .
f ( x)
� e
3x
, as
[6]
[3]
� � �
2. (a) By successive differentiation, find the Maclaurin series of f ( x) �ln tan �x
� �
� 4 � ,
as far as the term in
2
x .
(b) Hence, use this series to find an approximate value of ln 9.
[6]
[3]
3. (a) By successive differentiation, find the Maclaurin series of
as far as the term in
2
x .
(b) Hence, use this series to find an approximate value of f � (0.1) .
f x
1
� � ,
5
2
( ) ln(1 x )
[6]
[3]
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