Apps. and Interpretation for IBDP Maths Ebook 2 | Page 344

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Chapter 10
Exercise 41
41.1 ( a ) f �( x) �3 ( cos x � xsin x)
( b )
( i )
14.1
( ii )
�
0.0707
41.2
( a )
3x f �( x) �� 3e
( b )
( i )
�
2.22
( ii )
0.450
41.3
( a )
2 f �( x) �� 2xsin ( x
)
( b )
a �
1.25
41.4
( a )
g�( x) �2xln x � x
( b ) a � 1
Exercise 42
42.1 ( a ) f �( x) � 3cos3x
( b )
( i )
�
3
( ii )
y�
�3x�
3�
42.2
( a )
3 f�( x)
� x
( b )
( i )
3
( ii )
1
�
3
( iii )
1
1 y� � x� 3
3
42.3
( a )
3 f �( x) �
3e x
3 k
( b )
3 e
( c )
k �
1
42.4
( a )
1 f�( x)
�
2x
( b )
1
4
( c ) ln 2 � 8
Exercise 43
43.1 ( a )
43.2 ( a ) f �( x) � 9 � 6x � 3x
( b ) x �� 1 or x � 3 ( c ) ( i ) f ��( x) �6 � 6x
( ii )
�
1
( iii )
�
4
f �( x) �� xe �
1 x 2
( b )
x �
0
( c )
( i )
Refer to solution
( ii )
1
43.3
( a )
4�
4x f�( x)
�
3 ( x �1 )
( b )
x �
1
( c )
( i )
Refer to solution
( ii )
1
43.4
( a )
� f
� �
� ( x) �2cos
�2x �
� � 3
�
( b )
x �� 0.262 or x �
1.31
( c )
( i )
� �
� �4sin
�2x �
� � 3
�
( ii )
�
0.262
( iii )
�
4
Exercise 44
44.1 ( a ) n( 0 ) � 300
44.2 ( a )
( b )
( i )
dn
0.28t
84e dt
( ii )
451per month
( c ) 9
( b ) ( i )
3
V ( 8 ) � 6 cm
( ii )
2 dV t
�� dt 100 � t
2
3 1
0.75 cm s �
( c )
6
44.3
( a )
993
( b )
dp 500cos (
2t
3.9 ) dt
( c )
13
2
334
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