2017年AP微积分BC简答题真题+答案+PDF下载
1. A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height hfeet is given by the function A, where A(h) is measured in square feet. The function Ais continuous and decreases as h increases. Selected values for A(h) are given in the table above.
(a) Use a left Riemann sum with the three subintervals indicated by the data in the table to approximate the volume of the tank. Indicate units of measure.
(b) Does the approximation in part (a) overestimate or underestimate the volume of the tank? Explain your reasoning.
(c) The area, in square feet, of the horizontal cross section at height hfeet is modeled by the function f given by f(h)=50.3/e0.2h+h.Based on this model, find the volume of the tank. Indicate units of measure.
(d) Water is pumped into the tank. When the height of the water is 5 feet, the height is increasing at the rate of 0.26 foot per minute. Using the model from part (c), find the rate at which the volume of water is changing with respect to time when the height of the water is 5 feet. Indicate units of measure.
2. The figure above shows the polar curves r=f(θ)=1+sinθcos(2θ) and r=g(θ)=2cosθ for 0≤θ≤π/2.Let R be the region in the first quadrant bounded by the curve r=f(θ) and the x-axis. Let S be the region in the first quadrant bounded by the curve r=f(θ), the curve r=f(θ), and the x-axis.
(a) Find the area of R.
(b) The ray θ=k, where 0
(c) For each θ,0≤θ≤π/2,let w(θ)be the distance between the points with polar coordinates (f(θ),θ) and (g(θ),θ).Write an expression for w(θ). Find wA, the average value of w(θ)over the interval 0≤θ≤π/2.
(d) Using the information from part (c), find the value of θ for which w(θ)=wA. Is the function w(θ)increasing or decreasing at that value of θ? Give a reason for your answer.
2017年AP微积分BC简答题真题余下省略！
你可能还关注