The central finite difference approximation is written as:

$\frac{dP}{dx}=\frac{P(x+x)-P(x-x)}{2x}$

Please use the Taylor series method to prove that the central finite difference has a

second$-$order accuracy, $O(x^2),$ which means that its truncation error is proportional to the

value of $x^2.$please answer the following question in reference with the

table$/$code$$