$(5$ points$)$ A semicircle with diameter $PQ$ sits on an isosceles triangle $PQR$ to form a region shaped like a two$-$dimensional ice$-$cream cone, as shown in the figure. If $A()$ is the area of the semicircle and $B()$ is the area of the triangle, find

$\underset{0^{+}}{lim}\frac{A()}{B()}$

$(5$ points$)$ If two resistors with resistances $R_1$ and $R_2$ are connected in parallel, as shown in the figure, then the total resistance $R,$ measured in ohms $(),$ is given by

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

If $R_1$ and $R_2$ are increasing at rates of $0\mathrm{.}3\frac{}{s}$ and $0\mathrm{.}2\frac{}{s},$ respectively, how fast is $R$ changing when $R_1=30$ and $R_2=60?$