Analysis and Approaches for IBDP Maths Ebook 2 | Page 298

Your Practice Set – Analysis and Approaches for IBDP Mathematics
e � 2
(e) (1) An
�
n 1
e �
(2)
e � 2
An
�2 �
n�3
e
(3) Refer to solution
(f) � � 22
II (g) (1)
e�1 e�1
�B
2 1
�
2
2e
e
(2) Refer to solution
(3)
e�1 e�1
�B
3 2
� ,
3
2e
e
e�1 e�1
�B
4 3
�
4
2e
e
(4)
e�1 e�1
�B
n 1 n
�
�
n�1
2e
e
III (h) (1)
e �1
B1 � � A
2 1
e
(2) Refer to solution
(3) Refer to solution
(i) (1) Concave upward
(2) The area of A
n
is
always less than the
area of
B
n
(j) (1) 0
(2) Refer to solution
n n
n
e �1 e �1
IV (k) (1) � B
n�1 � k
�
n�1
2e
e
k�1
(2)
n
e �1 1
lim
n
n�1
�
�� e e
(3) Refer to solution
(l) (1)
1
e �1
(2) Refer to solution
(m) (1)
Bk
�
k 1
e � �
(2) Refer to solution
Exercise 81
81.1 (a) (1)
�
I(0)
�
2
(2) I(1) � 1
(3) Refer to solution
(4)
2
I(3)
�
3
(b) (1) Refer to solution
(2) Refer to solution
(c) (1) H(2) �I(0) � H(0)
(2) H(3) �I(1) � H(1)
(3)
H( n) �I( n �2)
�Hn
( �2)
(d)
� ( 2 �1)
H(4)
�
4
81.2 (a) Refer to solution
(b) (1)
1
d3
�
2
(2) Refer to solution
(3) Refer to solution
(4)
�
d5 � cos 5
(5) Refer to solution
(c) (1) Refer to solution
(2) A4 � 2
(d)
(3) Refer to solution
A �nd � d
2
n n( 1
n
)
(e) (1) Refer to solution
(2) lim A n
� �
n��
(3) The inscribed polygon
becomes a unit circle
and the shortest
distance of the
boundary of the
polygon to the origin
becomes the radius
1 as n tends to
positive infinity
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