Let f and g be the functions given by f(x) = e^x and g(x) = ln x.
(a) Find the area of the region encloed by the graphs of f and g between x = 1/2 and x = 1.
(b) Find the volume of the solid generated when the region eclosed by the graphs of f and g between x = 1/2 and x = 1 is revolved about the line y = 4.
(c) Let h be the function given h(x) = f(x) - g(x). Find the absolute minimum value of h(x) on the closed interval 1/2 less than or equal to x less than or equal to 1, and find the absolute maximum value of h(x) on the closed interval 1/2 less than or equal to x less than or equal to 1. Show the analysis that leads to your answer.
