2011年AP微积分BC简答题真题+答案+PDF下载
1. At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are not explicitly given. For t ≥ 0, dx/dt=4t+1 and sin(t2).At time t = 0, x(0) = 0 and y(0) = -4.
(a) Find the speed of the particle at time t = 3, and find the acceleration vector of the particle at time t = 3.
(b) Find the slope of the line tangent to the path of the particle at time t = 3.
(c) Find the position of the particle at time t = 3.
(d) Find the total distance traveled by the particle over the time interval 0 ≤ t ≤ 3.
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 ∫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BC简答题真题余下省略！
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