If x = -1.3 ± 0.002 and y = 2.17 ± 0.0009, find the error in the determination of the term x²-y²

We are given:
$x = -1.73$ with an absolute error $\Delta x = 0.002$
$y = 2.17$ with an absolute error $\Delta y = 0.009$
We need to find the error in the determination of the term $Z = x^2 - y^2$.

For a function $f(u) = u^n$, the absolute error is given by $\Delta f = |n u^{n-1}| \Delta u$.
For $x^2$:

For $y^2$:

When quantities are added or subtracted, their absolute errors add up to give the maximum possible absolute error.

The input errors (0.002 and 0.009) are given to one significant figure. It is common practice to round the final absolute error to one significant figure.

The error in the determination of the term $x^2 - y^2$ is $\boxed{0.05}$.