Question

find the relative error in z if z= a4b1/3/ c d3/2

Answer 1

The relative error in z is

 Δz/z = 4(Δa/a) +(1/3) (Δb/b) + (Δc/c) + (3/2) (Δd/d).

Answer 2

Answer:

The relative error in z can be found by the following the steps:

To find the relative error of any quantity or equation the power of that quantity is taken down and multiplied by that quantity containing particular power. These step is done for every individual quantity containing power and after this the power multiplied to the quantity are added or subtracted among according to the given condition, if there is percentage decrements then subtraction is done and if there is percentage increment then its added.

For the given equation the relative error according to the rule will be.

$\frac{\Delta z}{z}=4\left(\frac{\Delta a}{a}\right)+\frac{1}{3}\left(\frac{\Delta b}{b}\right)+\left(\frac{\Delta c}{c}\right)+\frac{3}{2}\left(\frac{\Delta d}{d}\right)$