1. Sand is leaking from the back of a dump truck and forming a conical pile on the ground. The sand is leaking at the rate of 0.7 m per hour. If the base radius of the pile is always 0.2 times the height, how fast is the base radius changing when the height is 1.1 m? Show all the working. (Volume of cone of height h and base radius r is V = rh.) 2. [7 marks] Let f(x)=6+ (2x-7) ln(2x-x+1) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(4.1). 3. [16 marks] Find the following integrals, showing all working. (a) 3x(x + 2)4/3 dr (b) 5x2 3 2 dr (t2 + 2e-t) dt (c) (d) fe e2+1 da 4. [6 marks] Water is being pumped into a cooling tank at the rate of V'(t) = 15t(221) 2 m per day, where t is the time in days since the pumping begins. Find the amount of water that flows into the tank during the third day. Give the answer exactly first and then to 4 significant figures. 5. [8 marks] Sketch the region bounded by f(x) = 2+ e, g(x) = 2 + 4e*, x = 0 and x=1. Using calculus, find the area of the region, showing all the working. Express your answer in simplified exact form.