1. [5 marks] Let f(x) = 3 + 9x2 ln(2 + 3:). Find the derivative of f and use it to estimate f(0.1). Give your answer exactly and accurate to 3 significant gures. Compare with the exact solution. 2. [8 marks] A farmer is lling a feed hopper with grain {while it is closed at the bottom). The hopper is an inverted cone (with the point at the bottom). The volume of a cone is V = %m'2h. Assume the radius of the hopper is equal to one half of the height. Suppose the farmer is adding 0.02m3/ s of grain. How quickly is the height of the grain changing (assuming it is level across the top) if the current height above the bottom is 0.5111? Show all working. 3. [14 marks] Find the following integrals, showing all working. (a) f x2(5x3 2}\"de xzil (b) I x3+31+7 [.11 (c) fol 2x1?\"2 dx 4. [8 marks] The farmer has taken grain to the local railyards to transport it for sale. The ow rate, F(t), in m3 / minute of the loader when unloading the truck is 2(1e-E) if0