$\mathop {\lim }\limits_{x \to 3} [x] = $,(where $[.]$ denotes the greatest integer function)

$\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x} = $

Let $f(x) = \lim_{y \to 0} \frac{(1 - \cos(xy))\tan(xy)}{y^3}$. Then the number of solutions of the equation $f(x) = \sin x, x \in R$ is:

$\lim _{x \rightarrow 0} \frac{a^x-1}{\sin (x)} = $

$\lim _{x \rightarrow-\infty} \frac{3|x|-x}{|x|-2 x} - \lim _{x \rightarrow 0} \frac{\log (1+x^3)}{\sin ^3 x} =$

If $f(x) = \begin{cases} \frac{\sin[x]}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer less than or equal to $x$,then $\lim_{x \to 0^-} f(x)$ is: