Analysis and Approaches for IBDP Maths Ebook 1 | Page 322

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 56
56.1 (b) 3a�b�
0
(c) a � 1, b �� 3
(d) (4, � 79)
56.2 (b) 75a�b�
0
(c) a � 2 , b �� 150
(d) (5, � 650)
56.3 (b) 20a�b�
0
(c) a � 3, b �� 60
(d)
7
ln 3
56.4 (b) 3a�b�
0
(c) a � 1, b �� 30
(d) (ln 5, �125 � 100ln 5)
Chapter 14
Exercise 57
57.1 y� �3x�
3�
57.2
57.3 1
57.4 2
2 �
1 � e �1
y� � x�
�
�e
Exercise 58
�e
58.1 (a) f ( �5) � 100 , f (0) � 0
(b) �5�
x � 1
(d) Refer to solution
58.2 (a) f (0) � 1, f (3) � 28
(b) �1�
x � 3
(d) Refer to solution
58.3 (a) 1
2
(b) f �( x) �� 2kxe (c)
(f)
�
2
�kx
�� � � �
f x ke kx
1
2
Refer to solution
2
( ) 2 (1 2 )
58.4 (a) 0
(b)
kx ( �1)
f�( x)
�
3
( x �1)
�2 kx ( �2)
f��( x)
�
4
( x �1)
(c) 4
(e) Refer to solution
Exercise 59
59.1 (a) 16sin�
(b)
�
� �
2
(c) 16
(d) � � 0 and � � �
59.2 (a) 100( � � 2sin 2 �)
(b)
�
� �
4
(c) 100( � � 2)
(d)
�
� � 0 and � �
2
59.3 (a) t � 0 and t � 6
(b) t � 2
(c) 0
(d) � 20
59.4 (a) 12
(b) t � 2
(c) 720
(d) 720
Exercise 60
60.1 (a) 39.8 m
(b) � 68.9 cms
60.2 (a) 1.52 m
(b)
-2
7.87 cms
t t
60.3 (a) 1�
e cos( e )
(b)
-2
117 cms
60.4 (a) 5.95 s
(b) � 11.2 cms
-2
-2
314
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