If $f(x)=\left\{\begin{array}{cc}\frac{\sin [x]}{[x]}, & {[x] \neq 0} \\ 0, & {[x]=0}\end{array}\right.$, where [.] denotes the greatest integer function, then $\lim _\limits{x \rightarrow 0} f(x)$ is equal to

$\lim _\limits{x \rightarrow 0} \frac{|\sin x|}{x}$ is equal to

If $f(x)=\left\{\begin{array}{ll}x^2-1, & 0< x< 2 \\ 2 x+3, & 2 \leq x < 3\end{array}\right.$, then the quadratic equation whose roots are $\lim _\limits{x \rightarrow 2^{-}} f(x)$ and $\lim_\limits{x \rightarrow 2^{+}}{f(x)}$ is

$\lim _{x \rightarrow 0} \frac{\tan 2 x-x}{3 x-\sin x}$ is equal to

If $f(x)=x-[x], \in R$, then $f^{\prime}\left(\frac{1}{2}\right)$ is equal to