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calculate the percentage error in the following A= X 3/2 ×Y 3 /Z −1/2 e following A= X 3 /2 * Y 3 ​/Z

calculate the percentage error in the following
 
A=    X3/2 ×Y3/Z−1/2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
e following
 
 
 
  • A=X3/2 * Y3​/Z
 

Grade:11

1 Answers

Susmita
425 Points
5 years ago
A=\frac{x^\frac{3}{2}×y^3}{z^\frac{1}{2}}
Take logarith on both sides.
logA=(3/2)logx+3logy-(1/2)logz
Take derivative.
\frac{dA}{A}=\frac{3}{2}\frac{dx}{x}+3\frac{dy}{y} -\frac{1}{2}\frac{dz}{z}
Relative error
 
|\frac{dA}{A}|=\frac{3}{2}|\frac{dx}{x}|+3|\frac{dy}{y} | + \frac{1}{2} |\frac{dz}{z}|
You can calculate its numerical value when relative errors in x,y,z are given.
Percentage error is
|dA/A|×100
Hope this helps.
Please approve if it does.
 

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