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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2017
/
Paper 1
/
15
/
c
/
i
/
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
2017
Paper 1
15
c
i
2026-10-18
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Use the
Maclaurin series
sin
x
=
x
−
x
3
/6
+
O
(
x
5
)
and
e
u
=
1
+
u
+
u
2
/2
+
u
3
/6
+
u
4
/24
+
O
(
u
5
)
. The terms through fourth degree give
e
s
i
n
x
=
1
+
(
x
−
6
x
3
)
+
2
1
(
x
2
−
3
x
4
)
+
6
x
3
+
24
x
4
+
O
(
x
5
)
=
1
+
x
+
2
x
2
−
8
x
4
+
O
(
x
5
)
.
(1)
In particular the cubic
coefficient
cancels; it has not been omitted accidentally.
Ancestors
(14)
i
c
15
Paper 1
2017
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
List of universities
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