Problem 56E

56. A semicircle with diameter $P Q$ sits on an isosceles triangle $P Q R$ to form a region shaped like a two-dimensional 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

$$ \lim _{\theta \rightarrow 0^{+}} \frac{A(\theta)}{B(\theta)} $$

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