2011年AP微积分AB简答题真题+答案+PDF下载
1. For 0 ≤ t ≤ 6, a particle is moving along the x-axis. The particle’s position, x(t), is not explicitly given.The velocity of the particle is given by v(t) = 2sin(et/4 ) + 1. The acceleration of the particle is given by a(t)=1/2et/4cos(et/4)and x(0) = 2.
(a) Is the speed of the particle increasing or decreasing at time t = 5.5 ? Give a reason for your answer.
(b) Find the average velocity of the particle for the time period 0 ≤ t ≤ 6.
(c) Find the total distance traveled by the particle from time t = 0 to t = 6.
(d) For 0 ≤ t ≤ 6, the particle changes direction exactly once. Find the position of the particle at that time.
2. As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for 0 ≤ t ≤ 10, where time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected values of time t are shown in the table above.
(a) Use the data in the table to approximate the rate at which the temperature of the tea is changing at time t = 3.5. Show the computations that lead to your answer.
(b) Using correct units, explain the meaning of 1/10∫100H(t)dt in the context of this problem. Use a trapezoidal sum with the four subintervals indicated by the table to estimate 1/10∫100H(t)dt
(c) Evaluate 1/10∫100H'(t)dt . Using correct units, explain the meaning of the expression in the context of this problem.
(d) At time t = 0, biscuits with temperature 100°C were removed from an oven. The temperature of the biscuits at time t is modeled by a differentiable function B for which it is known that B'(t)=-13.84e-0.173t.Using the given models, at time t = 10, how much cooler are the biscuits than the tea?
2011年AP微积分AB简答题真题余下省略！
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