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PARAGRAPH “A” If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. Forexample, consider the relation z =
. If the errors in x,y and z are Δ x , Δ y and Δ z ,respectively, then z ± Δ z =
=
( 1 ±
) ( 1 ±
) − 1 The series expansion for ( 1 ±
) − 1 ,to first power in Δ y / y , is 1 ∓ ( Δ y / y ) .The relative errors in independent variables are always added. So the error in z will be Δ z = (
+
)
The above derivation makes the assumption thatΔ x / x < < 1 , Δ y / y < < 1 .
Therefore, the higher power of these quantities are neglected.
(There are two questions based on PARAGRAPH “A”, the question given below)
The above derivation makes the assumption that
Therefore, the higher power of these quantities are neglected.
(There are two questions based on PARAGRAPH “A”, the question given below)
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