$\lim\limits_{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right)}{\sin ^2 x}$ equals

Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of points in $[\alpha,\beta]$ at which $f$ is not differentiable is

Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $\lim \limits_{n \rightarrow \infty} \frac{\left(a_n\right) n!}{{ }^{3 n} P_n}$ equals

$$ \text { Let } f(x)=\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1 \end{array}\right| \text {, then } \lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}= $$