Analysis and Approaches for IBDP Maths Ebook 2 | Page 294

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 63
63.1
63.2
63.3
63.4
2
x�2x
�
2 1 4
1 3 9 81
2 3
� x � x � x �
2
3x
3
x
Exercise 64
64.1 (a)
1 3
9 9
2 2
2 3
� x � x � x �
(b)
0.03
e � 1.0304545
64.2 (a) 2x �
(b)
2�
ln 9 �
3
64.3 (a)
1 2
5 x �
64.4 (a)
(b) f �(0.1) � 0.04
(b)
Exercise 65
�
�
2 x �
�
65.1 (a) (i)
(b)
(c)
65.2 (a) (i)
(b)
(c)
1.5
1
f ( t)dt ��0.982
ln 2�2
sec
tan x 2
(ln 2 � 2 tan x)
1 � (ln 2) x
(ii)
2
(ln 2) 2
� x �
2
11 36 86
2
� � x� x �
2
11
�
2
(ii)
2 4
1� x � x �
x
g( x) 1 x x
Refer to solution
Refer to solution
3 6
� � � �
65.3 (a) Refer to solution
(b) Refer to solution
65.4 (a) (i)
sec xtan
x
2
(6sec x �1)
(ii)
1
1 x 2
2
� �
1
(b) tan x x x
3
(c) 0.35625
Chapter 15
Exercise 66
66.1 (a)
3
� � �
cos t
x�
e ��
�
�� �
(b) e �x � e
66.2 y � 5
66.3
66.4
y �
y�
e
Exercise 67
2
4x�2sin 2x�1
ln 2x�3
1
67.1 y � � 2x
5
6x
�
1 x
67.2 y� x(2 � 1)
ln 2
67.3
y � x x �
2
cos (sin 3)
67.4 Refer to solution
Exercise 68
68.1 11.7
68.2 23.9
68.3 4.70
68.4 27.7
Exercise 69
69.1
y x x
2
�1�5 �11
�
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