2010年AP微积分AB简答题真题+答案+PDF下载
1. There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow accumulates on the driveway at a rate modeled by f (t) = 7tecost cubic feet per hour, where t is measured in hours since midnight. Janet starts removing snow at 6 A.M. (t = 6). The rate g(t), in cubic feet per hour,at which Janet removes snow from the driveway at time t hours after midnight is modeled by
(a) How many cubic feet of snow have accumulated on the driveway by 6 A.M.?
(b) Find the rate of change of the volume of snow on the driveway at 8 A.M.
(c) Let h(t) represent the total amount of snow, in cubic feet, that Janet has removed from the driveway at time t hours after midnight. Express h as a piecewise-defined function with domain 0 ≤ t ≤ 9.
(d) How many cubic feet of snow are on the driveway at 9 A.M.?
2. A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon (t = 0) and 8 P.M. (t = 8). The number of entries in the box t hours after noon is modeled by a differentiable function E for 0 ≤ t ≤ 8. Values of E(t), in hundreds of entries, at various times t are shown in the table above.
(a) Use the data in the table to approximate the rate, in hundreds of entries per hour, at which entries were being deposited at time t = 6. Show the computations that lead to your answer.
(b) Use a trapezoidal sum with the four subintervals given by the table to approximate the value of 1/8∫80E(t)dt.Using correct units, explain the meaning of 1/8∫80E(t)dt in terms of the number of entries.
(c) At 8 P.M., volunteers began to process the entries. They processed the entries at a rate modeled by the function P, where P(t) = t3 - 30t2 + 298t - 976 hundreds of entries per hour for 8 ≤ t ≤ 12. According to the model, how many entries had not yet been processed by midnight (t = 12) ?
(d) According to the model from part (c), at what time were the entries being processed most quickly? Justify your answer.
2010年AP微积分AB简答题真题余下省略！
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