$\lim\limits_{x \to 0}\dfrac{\tan x - x}{x^2(e^x - 1)}$.

设$f(x)=\begin{cases}a + x^2, & x \leq 0\\x\sin\dfrac{1}{x}, & x > 0\end{cases}$，在$x = 0$处连续，求$a$的值.

求不定积分$\int x^3\cos xdx$.