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

$\underset{x\to 0^{+}}{lim} x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\dots \dots +\left[\frac{15}{x}\right]\right)$

We know that $\left[x\right]=x-\left\{x\right\}$, where {x} denotes the fractional part of x.

$\begin{array}{r}\therefore \underset{x\to 0^{+}}{lim} x\left[\left(\frac{1}{x}+\frac{2}{x}+\dots +\frac{15}{x}\right)-\left(\left\{\frac{1}{x}\right\}+\left\{\frac{2}{x}\right\}+\dots +\left\{\frac{15}{x}\right\}\right)\right]\\ =\underset{x\to 0^{+}}{lim} (1+2+\dots +15)-\underset{x\to 0^{+}}{lim} x\left(\left\{\frac{1}{x}\right\}+\left\{\frac{2}{x}\right\}+\dots +\left\{\frac{15}{x}\right\}\right)\end{array}$

$=\frac{15(15+1)}{2}+0\times \mathrm{A}$ finite number less than 15=120