2021年AP微积分AB简答题真题+答案+PDF下载
1. The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the dish is given by an increasing, differentiable function f , where f(r) is measured in milligrams per square centimeter. Values of f(r) for selected values of r are given in the table above.
(a) Use the data in the table to estimate f'(2.25). Using correct units, interpret the meaning of your answer in the context of this problem.
(b) The total mass, in milligrams, of bacteria in the petri dish is given by the integral expression 2π∫40rf(r)dr. Approximate the value of 4 2π∫40rf(r)dr using a right Riemann sum with the four subintervals indicated by the data in the table.
(c) Is the approximation found in part (b) an overestimate or underestimate of the total mass of bacteria in the petri dish? Explain your reasoning.
(d) The density of bacteria in the petri dish, for 1≤r≤4, is modeled by the function g defined by g（r）=2 − 16(cos(1.57 √r))3. For what value of k , 1 < k < 4, is g(k) equal to the average value of g (r) on the interval 1 < r < 4 ?
2. A particle, P, is moving along the x-axis. The velocity of particle P at time t is given by vp(t) = sin(t1.5) for 0 ≤ t ≤ π. At time t = 0, particle P is at position x = 5.
A second particle, Q, also moves along the x-axis. The velocity of particle Q at time t is given by vQ (t) = (t-1.8)·1.25t for 0 ≤t ≤ π. At time t = 0, particle Q is at position x = 10.
(a) Find the positions of particles P and Q at time t = 1.
(b) Are particles P and Q moving toward each other or away from each other at time t = 1 ? Explain your reasoning.
(c) Find the acceleration of particle Q at time t = 1. Is the speed of particle Q increasing or decreasing at time t = 1 ? Explain your reasoning.
(d) Find the total distance traveled by particle P over the time interval 0≤t ≤ π.
2021年AP微积分AB简答题真题余下省略！
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