Analysis and Approaches for IBDP Maths Ebook 2 | Page 291

48.3
48.4
49.1
49.2
dz
4e
dt �
d�
� 1.5 rads
dt
Exercise 49
�1
3 2 2 6
ds
10t
d
�� ,
s 30 100
� �
t �
t
dt
s � 2 dt s �2 ( s �2)
d
2
s
22
�� ms
2
dt
25
t�
2
49.3 Refer to solution
49.4 (a) t � 0.652
(b) k �� 2
Exercise 50
50.1 (a)
CD
2 3
�2
1 11
x
4 4
1 3
H � x
8
11 137
2
� � x �
(b) (i)
2
� x �
4 8
(ii) 32.8
(iii) x � 4.49
(c)
d� 4 ��
2
dx
16 � x
(d)
50.2 (a)
(b)
�
2 2
(3x � 44x �137)(16 � x )
32
3 ( 36 48 13 2 3
� � x � x � x )
2
(i)
x
3 (48 26 3 2
� x�
x )
(ii)
250 3
27
(iii)
8
x �
3
(c) 3.06 �BC � 25
(d) The claim is disagreed
2
50.3 (a)
(b)
(c)
(d)
50.4 (a)
(b)
(c)
(d)
T �
(i)
(ii)
2
2x� 500 � x � 62500
4
2
2 x �62500
�x
2
4 x � 62500
233 s
500 3
(iii) x �
3
Refer to solution
The claim is agreed
2
�x
2
�� � �
g ( x) 2 e (2x
1)
Refer to solution
(i)
Chapter 12
Exercise 51
51.1 k � 7
51.2 k � 3
51.3 c � 9
51.4 k � 1
Exercise 52
2h�
2e
�
1 1
� �
2 2
2e
�2he
4
2
�h
(ii)
1 �
2
1 2
�h
� � he �
2 �
(iii) 0.597
(iv) h � 0.3054287
Refer to solution
52.1
1
�3 � ln 4
52.2 k � 8
52.3
1 2 1
� x cos 4x � xsin 4x
4 8
1
� cos 4 x�C
32
52.4 Refer to solution
1
2
e �
�
�
�
Answers
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