If function $f\left(x\right)$ is differentiable at $x=a,$ then $\underset{x\to a}{\lim }\frac{x^{2}f\left(a\right)-a^{2}f\left(x\right)}{x-a}$ is

$\underset{x\to \frac{\mathrm{\pi }}{2}}{\lim }\frac{\cot \left(x\right)-\cos \left(x\right)}{{\left(\mathrm{\pi }-2x\right)}^3}$ equals

For each $t\in R$, let $\left[t\right]$ be the greatest integer less than or equal to $\mathrm{t}.$ Then $\underset{x\to 0^{+}}{\lim }x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+ \dots +\left[\frac{15}{x}\right]\right)$

For each $t\in R,$ let $\left[t\right]$ be the greatest integer less than or equal to $t.$ Then,

$\underset{x\to 1^{+}}{lim}\frac{\left(1-\left|x\right|+\sin \left|1-x\right|\right)\sin \left(\frac{\pi }{2}\left[1-x\right]\right)}{\left|1-x\right|\left[1-x\right]}$