Question

If $Z=\frac{a{{b}^{2}}}{{{c}^{3}}}$ , then what is the error in Z? The errors in a, b, c are $\alpha$ , $\beta$ and $\gamma$ respectively

• A. $\alpha$ + 2 $\beta$ - 3 $\gamma$
• B. $\alpha$ - 2 $\beta$ + 3 $\gamma$
• C. 2 $\alpha$ + 3 $\beta$ + $\gamma$
• D. $\alpha$ + 2 $\beta$ + 3 $\gamma$

Answer 1

Answer: (D)

$\alpha$ + 2 $\beta$ + 3 $\gamma$

Answer 2

Maximum error in Z ${{\left| \frac{\Delta Z}{Z} \right|}_{\max }}=\frac{\Delta a}{a}+\frac{2\Delta b}{b}+\frac{3\Delta c}{c}$ $=\alpha +2\beta +3\gamma$