Physics

If $$X = A \times B$$ and $$\triangle X, \triangle A$$ and $$\triangle B$$ are maximum absolute errors in $$XA$$ and $$B$$ respectively, then the maximum relative error in X is given by:


ANSWER

$$\dfrac{\triangle X}X{} = \dfrac{\triangle A}{A} + \dfrac{\triangle B}{B}$$


SOLUTION
If $$X=A\times B$$
$$\Delta X,\Delta A,\Delta B$$ will be max absolute errors in $$XA$$ and $$B$$ relative error.
$$\cfrac{\Delta X}{X}=\cfrac{\Delta A}{A}+\cfrac{\Delta B}{B}$$
when the product value occur in any variable, the relative error will be summation value.
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