Analysis and Approaches for IBDP Maths Ebook 2

Your Practice Set – Analysis and Approaches for IBDP Mathematics Exercise 46 Exercise 47 46.1 (a) a � 0 (b) 1� 2x f�( x) � 2 1 � x (c) Refer to solution (d) (e) � 1 � 1 � 5 � �� , arctan �� ln � � 2 � 2 � 4 � f��( x) � 2 2(1 �x�x ) (1 � x ) 2 2 (f) Refer to solution (g) x � 0 or x � 1.17 46.2 (a) y � 2 (b) f �( x) � xe � 1 x 2 (c) Refer to solution (d) 1� y � 2 (e) (f) 2 1 x 2 2 f ��( x) �(1 � x ) e � Refer to solution (g) k �1� 2 e 46.3 (a) x �� 6, x � 6 (b) (c) (d) (e) (f) 2 36 � x f�( x) �� ( x � 36) 2 2 Refer to solution f��( x) � 2 2 xx ( �108) ( x � 36) 2 3 Refer to solution 1 gx ( ) � 2( x � 6) 46.4 (a) x �� 5, x � 5 (b) 100x f�( x) �� 2 2 ( x � 25) (c) (d) Refer to solution f��( x) � 2 100(3x � 25) ( x � 25) 2 2 3 (e) Refer to solution (f) (i) A �� 5, B � 5, C � 1 (ii) y � 1 47.1 (a) Refer to solution (b) 2 100 200 A� r � � � r r� (c) Refer to solution (d) k � 3 (e) 2 b � 3 47.2 (a) Refer to solution (b) r � 5 � (c) 125 5 3 V � r � � r 2 6 (d) Refer to solution (e) k � 9 47.3 (a) 1 2 2 2 V � �r ( R � R � r ) 3 (b) Refer to solution (c) Refer to solution (d) k � 32 (e) 76 3 81 R 47.4 (a) Refer to solution (b) (c) (d) (e) Exercise 48 2H V �Hx � x 2R Refer to solution 8 2 27 HR 8 (2 2 ) 9 R R � H 2 3 48.1 (a) dx 35 ms �1 �� dt 12 (b) d� 5 rads �1 � dt 24 48.2 (a) Refer to solution (b) dH � 41 dt 280 SE Production Limited

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