Analysis and Approaches for IBDP Maths Ebook 2

Your Practice Set – Analysis and Approaches for IBDP Mathematics 45 Paper 1 Section A – Equations of Tangents and Normals Example � � � � Show that the point � , 2 2 � � � on the curve e x�y � sin xy has a normal with equation x� y� 2� � 0. [7] Solution e x�y � sin xy d x� y d ( e ) � (sin xy) M1 dx dx x y dy dy ( e � � � ) 1 (cos xy) � � � � � � � �(1)( y) � ( x) � � � � A2 � dx� � � dx�� x�y x�y dy dy e � e � y cos xy � xcos xy dx dx x�y x�y dy dy e � y cos xy � e � xcos xy dx dx x�y x�y dy e � y cos xy � ( e � xcos xy) d x x� y dy e � y cos xy � A1 x� y dx e � xcos xy dy dx � e � � � 2 2 � � � � � � , � � 2 2 � 2 2 � � e � � � � 1� cos dy � 2 2 dx � � � � , � � � 2 2 � � � 1� cos 2 2 dy 1� 0 � d 1 � 0 x � � � � � , 2 2 � � � dy d x � � � � � , 2 2 � � � � 1 � � � � � cos� � � 2 � 2 2 � M1 � � � � � cos� � � 2 � 2 2 � 136 SE Production Limited

Analysis and Approaches for IBDP Maths Ebook 2 | Page 146