Analysis and Approaches for IBDP Maths Ebook 2 | Page 268

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Part III – Combining the Two Quantities
(i) (1) Express B
1
in terms of A
1.
1
(2) Show that B2 � � A2.
6
(3) Hence, show that
B
n
1
� �An.
nn ( �1)
(j) (1) State the concavity of the graph of f for x � 1.
(2) Hence, interpret the relationship between A
n
and
B
n
geometrically.
(k) (1) Write down
lim 1
n�� nn ( � . 1)
(2) Hence, show that lim A �lim B � 0 .
n��
n
n��
n
Part III Solution
(i) (1)
1
A1�B1
�
2
1
B1 � � A1
2
� 1 �
(2) A2 �B2
�2 � �
� 12 �
1
B2 � � A2
6
(3)
�� 1 � � 1��
An
� Bn
� (1) �� 4 � � �� 4 � ��
�� n�1� � n��
1 1
A � n
B � n
n
� n � 1
n�1�n
An
�Bn
�
nn ( �1)
B
n
1
� �A
nn ( �1)
n
258
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