The rate at which an albatross flaps its wings is dependent on its altitude. From measuring many albatrosses, it has been determined that the rate which an albatross flaps its wings is given by 1000 f (h) (1 + 9h)2' where h is the altitude in kilometres (km) and f(h) is in flaps per hour (flaps/h). If one bird has a particular trajectory where the altitude is a function of time h = h(t), where t is in hours, then the total number of flaps in T hours is given by F ( T) = ] f (h (t ) ) at One day, researchers observe an albatross with the following trajectory t (hours 0 1 2 3 4 5 6 7 8 h (km) 0.549 0.934 0.988 0.824 0.549 0.275 0.109 0.165 0.549 We wish to estimate the total number of flaps in 8 hours F(8). We will do this in two ways. (a) (5 points) Approximate f(h(t)) by a degree 2 polynomial centred at t = 0 using the chain rule. (b) (2 points) Use your answer in (a) to approximate F(8). (c) (2 points) Use a left-hand Riemann sum to approximate F(8). (d) (1 point) Compare your two answers. Which one do you expect to be more accurate? Why