P.o.t.W. #1 Solution
(a) The graph of \(f\left( x \right) = \sqrt {4 - {x^2}} is a semicircle with radius 2 units. Hence, the area bounded by the graph of \(f and the x-axis is \(\frac{1}{2}\pi{r^2} = \frac{1}{2}\pi{2^2} = 2\pi\;\;{\textrm{unit}}{{\textrm{s}}^2} . (b) (i) For any value of \(p the graph of \(g\left( x \right) = \sqrt {\frac{x + 2}{p}} will contain the point \(\left( { - \,2,0} \right) . Below are graphs of g for \(p = 1...