Test an equation for exactness

You will write three small functions. The first estimates a partial derivative. The second tests whether $M\,dx + N\,dy = 0$ is exact. The third finds the change in the solution function $F$ between two points, by adding up thin strips.

The idea. The partial derivative $\dfrac{\partial M}{\partial y}$ is the slope of $M$ when only $y$ changes. Estimate it from two nearby values: $\dfrac{M(x, y + h) - M(x, y - h)}{2h}$. The equation is exact when $M_y = N_x$ at every point. The change in $F$ from $(x_0, y_0)$ to $(x_1, y_1)$ has two parts. The first is the integral of $M$ along the line $y = y_0$ from $x_0$ to $x_1$. The second is the integral of $N$ along the line $x = x_1$ from $y_0$ to $y_1$.

Your tasks.

1. Finish slope_in_y(f, x, y). Return the estimate above, with h = H.
2. Finish is_exact(M, N, points). Return True when $M_y$ and $N_x$ differ by less than 0.001 at every point in the list. For $N_x$ you need a slope in $x$, which slope_in_x already gives.
3. Finish change_in_F(M, N, x0, y0, x1, y1). Use the midpoint rule with n = 2000 strips for each of the two integrals.