SECTION II, Part A
A graphing calculator is required for some problems or parts of problems.
1）There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow accumulates on the driveway at a rate modeled by f(t)=7tecos t cubic feet per hour, where t is measured in hours since midnight. Janet starts removing snow at 6 A.M. (t=6.) The rate g(t), in cubic feet per hour, at which Janet removes snow from the driveway at time t hours after midnight is modeled by
How many cubic feet of snow have accumulated on the driveway by 6 A.M.?
Find the rate of change of the volume of snow on the driveway at 8 A.M.
Let h(t) represent the total amount of snow, in cubic feet, that Janet has removed from the driveway at time t hours after midnight. Express h as a piecewise-defined function with domain 0 ≤t ≤9.
How many cubic feet of snow are on the driveway at 9 A.M.?
2） A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon (t = 0) and 8 P.M. (t = 8). The number of entries in the box t hours after noon is modeled by a differentiable function E for 0≤ t ≤ 8. Values of E(t), in hundreds of entries, at various times t are shown in the table above.
(a) Use the data in the table to approximate the rate, in hundreds of entries per hour, at which entries were being deposited at time t = 6. Show the computations that lead to your answer.
(d) According to the model from part (c), at what time were the entries being processed most quickly? Justify your answer.
a、Find the speed of the particle at time t =3 seconds.
b、Find the total distance traveled by the particle for 0 ≤t ≤ 4 seconds.
c、Find the time t, 0 ≤t≤4, when the line tangent to the path of the particle is horizontal. Is the direction of motion of the particle toward the left or toward the right at that time? Give a reason for your answer.
d、There is a point with x-coordinate 5 through which the particle passes twice. Find each of the following.
i The two values of t when that occurs
ii The slopes of the lines tangent to the particle’s path at that point
iii The y-coordinate of that point, given y 2 =3+1/e
SECTION II, Part B部分
|完成AP微积分BC阶段的知识点的学习。通过系统地梳理，充分的练习熟悉考试的题型和难点重点，冲5分。||课次1-2||Derivatives I &Application of Derivatives I||
Application of Derivatives II&
The Definite Integral
Differential Equation &
Application of Definite Integrals
L' Hôpital's Rule, Improper
Parametric vector, Polar functions
Infinite series I&
Infinite series II