Question

Solve ASAP . And ONLY FOR CLASS XI AND XII STUDENTS .

Answer 1

Answer:

⇒ Percentage error in Z = $100[(\frac{1}{3})(\frac{\Delta A}{A}) + (4)(\frac{\Delta B}{B}) + (1)(\frac{\Delta C}{C}) + (\frac{2}{3})(\frac{\Delta D}{D})]$

Explanation:

Given :

To find error percent of Z,

if Z = $\frac{A^{\frac{1}{3}}B^4}{CD^{\frac{2}{3} }}$

Solution :

Let relative error of A = $\frac{\Delta A}{A}$

Let relative error of B = $\frac{\Delta B}{B}$

Let relative error of C = $\frac{\Delta C}{C}$

Let relative error of D = $\frac{\Delta D}{D}$

We know that,

Error in $A^x = x(\frac{\Delta A}{A})$

Hence,

Error in $A^{\frac{1}{3}} = (\frac{1}{3})(\frac{\Delta A}{A})$

Error in $B^{4} = (4)(\frac{\Delta B}{B})$

Error in $C^{1} = (1)(\frac{\Delta C}{C})$

Error in $D^{\frac{2}{3}} = (\frac{2}{3})(\frac{\Delta D}{D})$

As, they are in division,.

⇒ Error in Z = $\frac{\Delta Z}{Z} = (\frac{1}{3})(\frac{\Delta A}{A}) + (4)(\frac{\Delta B}{B}) + (1)(\frac{\Delta C}{C}) + (\frac{2}{3})(\frac{\Delta D}{D})$

⇒ Percentage error in Z = $100[(\frac{1}{3})(\frac{\Delta A}{A}) + (4)(\frac{\Delta B}{B}) + (1)(\frac{\Delta C}{C}) + (\frac{2}{3})(\frac{\Delta D}{D})]$