2014年AP微积分AB简答题真题+答案+PDF下载

Section II，Part A

(a) Find all values of t in the interval 2≤t≤ 4 for which the speed of the particle is 2.

(b) Write an expression involving an integral that gives the position s（t）. Use this expression to find the position of the particle at time t=5.

(c) Find all times t in the interval 0≤t≤5 at which the particle changes direction. Justify your answer.

(d) Is the speed of the particle increasing or decreasing at time t=4? Give a reason for your answer.

2.

 Let R be the region enclosed by the graph of f(x)=and the horizontal line y=4, as shown in the figure above.
(a) Find the volume of the solid generated when R is rotated about the horizontal line y=-2.
(b) Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in R. Find the volume of the solid.
(c) The vertical line x=k divides R into two regions with equal areas. Write, but do not solve, an equation involving integral expressions whose solution gives the value k

SECTION II, Part B部分

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