Let $\left[x\right]$ denote the greatest integer less than or equal to $x$ . Then $\underset{x\to 0}{\mathrm{l}\mathrm{i}\mathrm{m}}\frac{\mathrm{t}\mathrm{a}\mathrm{n}\left(\pi {\mathrm{s}\mathrm{i}\mathrm{n}}^{2}x\right)+{\left(\right|x|-\mathrm{s}\mathrm{i}\mathrm{n}(x\left[x\right]\left)\right)}^2}{x^2}$ 

Let $f\left(x\right)$ be a polynomial of degree four and having its extreme values at $x=1$ and $x=2$. If $\underset{x\to 0 }{\lim }\left[1+\frac{\mathrm{f}\left(x\right)}{x^2}\right]=3$, then $f\left(2\right)$ is equal to