Analysis and Approaches for IBDP Maths Ebook 2 | Page 213

4. The function f is given by f ( x) � sec x .
(a) (i) Find the first three derivatives of f( x ).
(b)
(c)
(ii) Hence, find the Maclaurin series for f( x ) up to and including the
term.
[9]
By using the Maclaurin series for sin x , find the Maclaurin series for tan x up to
3
and including the x term.
[5]
Hence, find an approximate value of the area of the region enclosed by the graph
of g( y) � y tan y , the y -axis and the lines y � 0.5 and y � 1.
3
x
[4]
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