Consider the ratio to be determined by measuring a dimensionless quantity

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Applications and Interpretation · Number and Algebra · Number and Algebra

Problem

Consider the ratio

r = \frac{(1-a)}{(1+a)}

to be determined by measuring a dimensionless quantity

a

. If the error in the measurement of

a

\Delta a

(

\Delta a/a \ll 1

), then what is the error

\Delta r

in determining

r

? (1)

\frac{\Delta a}{(1+a)^2}

(2)

\frac{2\Delta a}{(1+a)^2}

(3)

\frac{2\Delta a}{(1-a^2)}

(4)

\frac{2a\Delta a}{(1-a^2)}