3. Let f be the function defined by f (x) = -2. Let S be the shaded region bounded by the graph of f and the horizontal line y = 1, as shown in the figure above. a. Find the area of S. (3.5 pts) . Write, but do not evaluate, an integral expression for the volume of the solid generated when S is rotated about the horizontal line y = 4. (2.5 pts) c. Let h(x) be the vertical distance between the point (x, f(x)) and the horizontal line y = 1. Find the rate of change of h(x) with respect to x at x = 2 (3 pts) d. S is the base of a solid with rectangular cross sections perpendicular to the y-axis. The rectangles have height double their base. Write, but do not solve, an integral expression for the volume of this solid. (3 pts)4. In a factory, the function y = f(t) models the amount of liquid in a tank, in gallons, at time t seconds. At time t = 0 there are 10 grams of liquid in the tank. Liquid flows both in and out of the tank such that the function y = f(t) satisfies the differential equation ax =- 0. 02y. a. Use the line tangent to the graph of y = f(t) at t = 0 to approximate the amount of liquid in the tank at time t = 2.5 seconds. (3 pts) b. Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. (1.5 pts) c. Find an expression y = f(t) by solving the differential equation at =- 0. 02y with the initial condition f(0) = 10. (4.5 pts) d. Determine whether the amount of liquid in the tank is changing at an increasing or a decreasing rate. Explain your reasoning. (2 pts)