若$f(x)=\begin{cases}\sin x, & x < 0\\-ax, & x\geq0\end{cases}$在$x = 0$处可导，求$a$的值.

设由方程$e^{xy}-xy^{2}=e^{2}$确定的函数为$y = y(x)$，求$\left.\dfrac{dy}{dx}\right|_{x = 0}$.

$\lim\limits_{x \to +\infty}(\sqrt{x + 2}-\sqrt{x - 3})$.