A semicircle with diameter $PQ$ sits on an isosceles triangle $PQR$ to form a region shaped like an ice cream cone, as shown in the figure. If $A(\theta)$ is the area of the semicircle and $B(\theta)$ is the area of the triangle, find $\displaystyle\lim_{\theta \to 0^{+}} \frac{A(\theta)}{B(\theta)}$.

$\displaystyle\lim_{\theta \to 0^{+}} \frac{A(\theta)}{B(\theta)}=$