Question

If percentage error in a, b and c are 2%. 1% and
3% respectively in given expression. Find
percentage error in x
X=a√ab²÷3√c with solution.....​

Answer 1

Answer:

1. 2sqroot2÷3sqroot3 , then squaring both sides ,. 4*2÷9*3=ans- 8÷27

Explanation:

a=2,b=1, c=3

put in eqn

2*sqroot2*1^2÷3*sqroot3.

Answer 2

The percentage error in x = a√(ab²) ÷ 3√c is ± 5 %.

Given: The percentage error in a, b and c are 2%, 1%, and 3% respectively

To Find: The percentage error in x = a√(ab²) ÷ 3√c

Solution:

• Now, from the rules of propagation of error we know that, the percentage error can be calculated by writing an expression with addition irrespective of the multiplication or division present in the original expression.

• Whenever there is a power in the original expression, it shall be written in front of the variable in the error expression.

The express given is,

      x = a√(ab²) ÷ $\sqrt[3]{c}$

This can be written as,

 ⇒ Δx / x = ± [ Δa / a + 1/2 × [ Δa / a + 2 × Δb / b ] +  1/3 Δc / c ]

It is given that Δa / a = 2 %, Δb / b = 1 % and Δc / c = 3 %

Putting these values in the respective places, we get;

⇒ Δx / x = ± [ 2 % + 1/2 × [ 2 % + 2 × 1 % ] +  1/3 × 3 % ]

               = ± [ 2 % + 2 % +  1 % ]

               = ± 5 %

Hence, the percentage error in x = a√(ab²) ÷ 3√c is ± 5 %.

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