AP Calculus Slides February 29, 2008

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Workshop style review of applications of integrals.

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AP Calculus Slides February 29, 2008

  1. 1. Applications of the Integral Workshop Cal. Lab
  2. 2. (1) At what time does the object attain its maximum acceleration? (a) 2 < t < 5 (b) 5 < t < 8 (c) t = 6 (d) t = 8 (e) 8 < t < 9
  3. 3. (2) The object is farthest from the starting point at t = (a) 2 (b) 5 (c) 6 (d) 8 (e) 9
  4. 4. (3) At t = 8 the object was at position x = 10. At t = 5, the position was x = (a) -5 (b) 5 (c) 7 (d) 13 (e) 15
  5. 5. Greater Boston can be approximated by a semicircle of radius 8 miles with its centre on the coast. Moving away from the centre along a radius, the population density is constant for the first mile. Beyond that, the density starts to decrease according to the data given in the table, where ρ(r), thousands/mile2, is the population density at a distance r miles from the centre. (a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius. (b) Determine a possible formula for ρ(r). Use this formula to make another estimate of the population.
  6. 6. (a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius.
  7. 7. (a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius.
  8. 8. These are the answers, although they are not necessarily in the correct order. ;-)

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