2 -2 0 4 6 -2 2. The function f is defined on the closed interval [-4,9]. The graph of f consists of a semicircle, a quarter circle, and three linear segments, as shown in the figure above. Let g be the function defined by g(x) = 3x + /2 f(t) dt. (a) Find g(8) and g'(8). (b) Find the value of x in the closed interval [-4,9] at which g attains its maximum value. Justify your answer. (c) Find lim f'(x), or state that it does not exist. Justify your answer. x-2 (d) Find lim 8g(2x) -27 - 160 x - 3 ex-3 - 1 For each problem: draw a diagram and setup an integral expression you would use. Then solve the problem without using a calculator. 3. The region bounded by the curve y = e" and the x-axis is between x = 0 and x = 1 is revolved around the x-axis. Find the volume of this solid of revolution. 4. The region bounded by the curvesy =x and y = x is rotated about the liney = 3. Compute the volume of the resulting solid