Analysis and Approaches for IBDP Maths Ebook 2 | Page 185

57
Paper 1 Section B – Analysis of Functions
Example
Consider the function f ( x) � cosec�
x , � � �
x
�
� � �
, x � 0 . The graph of f has a local
1
minimum point at x � .
4
13
(a) Show that � � 2�
.
(b)
(c)
Show that f is an odd function.
State the largest possible domain of f such that
(d) Write down the range of f .
The region bounded by the curve
1
f �
exists.
y� cosec�
x and the lines x� a and
1
x � , where
4
1
0 �a
� , is rotated through 2π radians about the x -axis. The volume of the solid
4
[2]
[2]
[2]
[1]
generated is 1 2 .
(e) Find the value of a .
[8]
1
The region bounded by the curve y� cosec�
x and the lines x� b and x �� , where
4
�1� b � 0, is rotated through 2π radians about the x -axis. The volume of the solid
generated is 1 2 .
(f) Write down the possible values of b .
[2]
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