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Mathematics
Problem
Consider the ratio
r
=
(
1
−
a
)
(
1
+
a
)
r = \frac{(1-a)}{(1+a)}
r
=
(
1
+
a
)
(
1
−
a
)
to be determined by measuring a dimensionless quantity
a
a
a
. If the error in the measurement of
a
a
a
is
Δ
a
\Delta a
Δ
a
(
Δ
a
/
a
≪
1
\Delta a/a \ll 1
Δ
a
/
a
≪
1
), then what is the error
Δ
r
\Delta r
Δ
r
in determining
r
r
r
? a.
Δ
a
(
1
+
a
)
2
\frac{\Delta a}{(1+a)^2}
(
1
+
a
)
2
Δ
a
b.
2
Δ
a
(
1
+
a
)
2
\frac{2\Delta a}{(1+a)^2}
(
1
+
a
)
2
2Δ
a
c.
2
Δ
a
(
1
−
a
2
)
\frac{2\Delta a}{(1-a^2)}
(
1
−
a
2
)
2Δ
a
d.
2
a
Δ
a
(
1
−
a
2
)
\frac{2a\Delta a}{(1-a^2)}
(
1
−
a
2
)
2
a
Δ
a
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