Question

$\dag\;\sf \pink{Hi\;there!\;:D}$
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If absolute error in quantity A is ∆A and in B is ∆B, then maximum absolute error in calculation of (A - B) will be

A) ∆A - ∆B

B) ∆B - ∆A

C) ∆A/A + ∆B/B

D) ∆A + ∆B
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Thanks!☃️ :D​

Answer 1

Answer:

Error in A + B = ±ΔA ±ΔB

max error in A + B = ∆A + ∆B

Explanation:

Z = A/B

=> Z ± ∆Z = (A±ΔA / B±ΔB)

=(A/B) (1 ± ∆A/A)/(1 ± ∆B/B)

=> 1 ± ∆Z/Z = (1 ± ∆A/A)(1 ± ∆B/B)^-1

=> 1 ± ∆Z/Z= (1 ± ∆A/A) (1 -+ ∆B/B)

=> ± ∆Z/Z = ± ∆A/A -+ ∆B/B

=> ∆Z/Z = ∆A/A + ∆B/B