2016年AP微积分AB简答题真题+答案+PDF下载
1. Water is pumped into a tank at a rate modeled by W(t)=2000e-t2/20 liters per hour for 0≤t≤8, where t is measured in hours. Water is removed from the tank at a rate modeled by R(t) liters per hour, where R is differentiable and decreasing on 0≤t≤8. Selected values of R(t) are shown in the table above. At time t=0, there are 50,000 liters of water in the tank.
(a) Estimate R'(2). Show the work that leads to your answer. Indicate units of measure.
(b) Use a left Riemann sum with the four subintervals indicated by the table to estimate the total amount of water removed from the tank during the 8 hours. Is this an overestimate or an underestimate of the total amount of water removed? Give a reason for your answer.
(c) Use your answer from part (b) to find an estimate of the total amount of water in the tank, to the nearest liter, at the end of 8 hours.
(d) For 0≤t≤8, is there a time t when the rate at which water is pumped into the tank is the same as the rate at which water is removed from the tank? Explain why or why not.
2. For t≥0, a particle moves along the x-axis. The velocity of the particle at time t is given by v(t)=1+2sin(t2/2). The particle is at position x=2 at time t=4.
(a) At time t=4, is the particle speeding up or slowing down?
(b) Find all times t in the interval 0
(c) Find the position of the particle at time t=0.
(d) Find the total distance the particle travels from time t=0 to time t=3.
3. The figure above shows the graph of the piecewise-linear function f. For -4≤x≤12, the function g is defined by g(x)=∫x2f(t)dt.
(a) Does g have a relative minimum, a relative maximum, or neither at x=10? Justify your answer.
(b) Does the graph of g have a point of inflection at x=4? Justify your answer.
(c) Find the absolute minimum value and the absolute maximum value of g on the interval -4≤x≤12.Justify your answers.
(d) For -4≤x≤12, find all intervals for which g(x)≤0.
2016年AP微积分AB简答题真题余下省略！
你可能还关注