2019年AP微积分BC简答题真题+答案+PDF下载
1. Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 20.1t2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).
(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ? Give your answer to the nearest whole number.
(b) What is the average number of fish that leave the lake per hour over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5) ?
(c) At what time t, for 0≤t≤8, is the greatest number of fish in the lake? Justify your answer.
(d) Is the rate of change in the number of fish in the lake increasing or decreasing at 5 A.M. (t = 5) ? Explain your reasoning.
2. Let S be the region bounded by the graph of the polar curve r(θ)= 3√θ sin(θ2) for 0≤θ≤√π, as shown in the figure above.
(a) Find the area of S.
(b) What is the average distance from the origin to a point on the polar curve r(θ) = 3√θ sin(θ2) for 0 ≤ θ ≤ √π ?
(c) There is a line through the origin with positive slope m that divides the region S into two regions with equal areas. Write, but do not solve, an equation involving one or more integrals whose solution gives the value of m.
(d) For k > 0, let A(k) be the area of the portion of region S that is also inside the circle r = k cosθ. Find limk→∞ A(k).
2019年AP微积分BC简答题真题余下省略！
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