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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 10
Total: 71
If
x
is so small that
x
3
and higher powers of
x
may be neglected, then
(
1
+
x
)
3
2
−
(
1
+
1
2
x
)
3
(
1
−
x
)
1
2
may be approximated as
1
−
3
8
x
2
3
x
+
3
8
x
2
−
3
8
x
2
x
2
−
3
8
x
2
Validate
Solution:
(
1
+
x
)
3
2
=
1
+
3
2
x
+
3
2
⋅
1
2
1.2
x
2
+
.
.
.
=
1
+
3
2
x
+
3
8
x
2
(As
x
is so small, so
x
3
and higher powers of
x
neglected)
(
1
+
x
)
3
2
−
(
1
+
1
2
x
)
3
(
1
−
x
)
1
2
=
(
1
+
3
2
x
+
3
8
x
2
)
−
(
1
+
3
C
0
⋅
x
2
+
3
C
1
⋅
(
x
2
)
2
)
(
1
−
x
)
2
=
3
8
x
2
−
3
4
x
2
(
1
−
x
)
2
=
x
2
(
3
8
−
3
4
)
(
1
−
x
)
−
2
=
−
3
8
x
2
(
1
−
1
2
(
−
x
)
+
.
.
.
.
)
=
−
3
8
x
2
−
3
16
x
3
[ As
x
3
is so small we can ignore
−
3
16
x
3
]
=
−
3
8
x
2
© examsnet.com
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