I’m new to stochastic differential equations, and I recently encountered the following problem:
Consider an SDE
$$dX_t = b(X_t)dt + sigma(X_t)dw$$
where $X_0 = x$ and $tin (0, T)$. Show the following:

$$lim_{tto s} Eleft(frac{X_t – X_s}{t – s} mid X_s = xright) = b(x, s)$$

$$lim_{tto s} Eleft(frac{(X_t – X_s)(X_t – X_s)^T}{t – s} mid X_s = xright) = Sigma(x, s)$$
Here, $Sigma(x, s)$ denotes the diffusion matrix and $b(x, s)$ is called the drift.
I’m pretty lost on this problem. I’m not really even sure where to begin. The first expression reminds me of the definition of a derivative, but I can’t quite see how to solve this exercise, so I thought I’d ask here