Question

if Z=A/B then maximum absolute error in Z will be​

Answer 1

Given : The expression, Z = A/B

To find : The maximum error in Z.

solution : Given expression, Z = A/B

Taking logarithm both sides we get,

logZ = log(A/B)

from properties of logarithm,

Log(A/B) = logA - logB

⇒logZ = logA - logB

differentiating both sides we get,

dZ/Z = dA/A - dB/B

putting, dZ = ± ∆Z , dA = ±∆A, dB = ± ∆B

⇒±∆Z/Z = ±∆A/A -+ ∆B)/B

for getting maximum absolute error, take only positive terms.

i.e., ∆Z/Z = ∆A/A + ∆B/B

⇒∆Z = Z(∆A/A + ∆B/B)

Therefore maximum absolute error in Z will be Z(∆A/A + ∆B/B)

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Answer 2

Answer:

Z= ∆A/A+∆B/B is the correct option

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