22. Let $s$ be a square with side length $x$. If the change in side length from $x_{0}$ to $x_{0}+h$ is approximated by $\frac{\mathrm{d} A}{\mathrm{~d} x}\left(x_{0}\right) \cdot h$ for the change in area of $S$, then the absolute error of this approximation is ( ).
(A) $h^{2}$
(B) $2 h x_{0}$
(C) $x_{0}^{2}$
(D) $h$
$(\mathrm{F}) *$
22. (A).

Since the area of $S$ is $A(x)=x^{2}$. Then when $x$ changes from $x_{0}$ to $x_{0}+h$, the absolute value of the change in $A(x)$ is
$$
A\left(x_{0}+h\right)-A\left(x_{0}\right)=\left(x_{0}+h\right)^{2}-x_{0}^{2}=2 h x_{0}+h^{2} \text {. }
$$

Also, $\frac{\mathrm{d} A}{\mathrm{~d} x}\left(x_{0}\right) \cdot h=2 x_{0} h$ is the approximate value of the change in $A(x)$. Therefore, the absolute error is $h^{2}$.