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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2011
/
Paper 1
/
11
/
b
/
iii
/
Solution
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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
2011
Paper 1
11
b
iii
2026-10-18
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Use
sin
x
=
x
−
x
3
/6
+
O
(
x
5
)
inside the
exponential series
:
e
s
i
n
x
=
1
+
(
x
−
6
x
3
)
+
2
x
2
+
6
x
3
+
O
(
x
4
)
.
(1)
The two cubic contributions cancel, leaving
e
s
i
n
x
=
1
+
x
+
2
x
2
+
O
(
x
4
)
.
(2)
Thus the
coefficient
of
x
3
is zero, even though the
function
itself is not an
even function
.
Ancestors
(14)
iii
b
11
Paper 1
2011
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
Mathematics course of the year 1 of the natural sciences course of the University of Cambridge
Year 1 of the natural sciences course of the University of Cambridge
Year of the natural sciences course of the University of Cambridge
Natural sciences course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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