2019年AP微积分AB简答题真题+答案+PDF下载
1. Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t)=4+20.1t2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).
(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ? Give your answer to the nearest whole number.
(b) What is the average number of fish that leave the lake per hour over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ?
(c) At what time t, for 0≤t≤8, is the greatest number of fish in the lake? Justify your answer.
(d) Is the rate of change in the number of fish in the lake increasing or decreasing at 5 A.M. (t = 5) ? Explain your reasoning.
2. The velocity of a particle, P, moving along the x-axis is given by the differentiable function vP , where vP(t) is measured in meters per hour and t is measured in hours. Selected values of vP(t) are shown in the table above. Particle P is at the origin at time t = 0.
(a) Justify why there must be at least one time t, for 0.3≤t≤2.8, at which vP'(t), the acceleration of particle P, equals 0 meters per hour per hour.
(b) Use a trapezoidal sum with the three subintervals [0, 0.3], [0.3, 1.7], and [1.7, 2.8] to approximate the value of∫2.80 vP(t)dt.
(c) A second particle, Q, also moves along the x-axis so that its velocity for 0≤t≤4 is given by vQ(t)=45√t cos(0.063t2) meters per hour. Find the time interval during which the velocity of particle Q is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 60 meters per hour.
(d) At time t = 0, particle Q is at position x = −90. Using the result from part (b) and the function vQ from part (c), approximate the distance between particles P and Q at time t = 2.8.
2019年AP微积分AB简答题真题余下省略！
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