Question

Given $A=\frac{x^p}{y^q{z}^r}$. The percentage errors in measurement of $x,y$ and $z$ are 1 %, 0.5 % and 2% respectively. If $p=3,q=2$ and $r=1$ then the maximum percentage error in A is

• A. $5$ %
• B. $6$ %
• C. $3$ %
• D. None of these

Answer 1

The correct option is B $6$ %

Given, $A=\frac{x^p}{y^q{z}^r}$
Take ln and then differentiate , $\frac{\Delta A}{A}=\pm (p\frac{\Delta x}{x}+q\frac{\Delta y}{y}+r\frac{\Delta z}{z})$
Thus the maximum percentage error in A:
$\frac{\Delta A}{A}\times 100=p\frac{\Delta x}{x}\times 100+q\frac{\Delta y}{y}\times 100+r\frac{\Delta z}{z}\times 100=(3\times 1)+(2\times 0.5)+(1\times 2)=6$ %