2013年AP微积分AB简答题真题+答案+PDF下载
1. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant is modeled by G(t)=90+45cos(t2/18),where t is measured in hours and 0≤t≤8. At the beginning of the workday(t=0), the plant has 500 tons of unprocessed gravel. During the hours of operation, 0≤t≤8, the plant processes gravel at a constant rate of 100 tons per hour.
(a) Find G'(5). Using correct units, interpret your answer in the context of the problem.
(b) Find the total amount of unprocessed gravel that arrives at the plant during the hours of operation on this workday.
(c) Is the amount of unprocessed gravel at the plant increasing or decreasing at time t=5 hours? Show the work that leads to your answer.
(d) What is the maximum amount of unprocessed gravel at the plant during the hours of operation on this workday? Justify your answer.
2. A particle moves along a straight line. For 0≤t≤5, the velocity of the particle is given by v(t)=-2+(t2+3t)6/5-t3 , and the position of the particle is given by s(t). It is known that s(0)=10.
(a) Find all values of t in the interval 2≤t≤4 for which the speed of the particle is 2.
(b) Write an expression involving an integral that gives the position s(t). Use this expression to find the position of the particle at time t=5.
(c) Find all times t in the interval 0≤t≤5 at which the particle changes direction. Justify your answer.
(d) Is the speed of the particle increasing or decreasing at time t=4 ? Give a reason for your answer.
2013年AP微积分AB简答题真题余下省略！
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