Answer
Thus, $(2.93^{2}-0.94^{2})^{1/3} = 2+(-0.025)= 1.975$
Calculator $(2.93^{2}-0.94^{2})^{1/3} \approx1.9748$
The error is approximately 0.0002
Work Step by Step
We are given $(2.93^{2}-0.94^{2})^{1/3}$
We know that $(3^{2}-1^{2})^{1/3}=2$. Therefore, let $x=3, dx=-0.07,y=1,dy=-0.06$
$dz=f_{x}(x,y).dx+f_{y}(x,y).dy$
$dz=(\frac{(x^{2}-y^{2})^{-2/3}.2x}{3})dx+(\frac{(x^{2}-y^{2})^{-2/3}.(-2y)}{3})dy$
$dz=\frac{1}{2}dx-\frac{1}{6}dy$
$dz\approx -0.025$
Thus, $(2.93^{2}-0.94^{2})^{1/3} = 2+(-0.025)= 1.975$
Calculator $(2.93^{2}-0.94^{2})^{1/3} \approx1.9748$
The error is approximately 0.0002
