AP® Calculus AB
2007 Scoring Guidelines
Form B
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Question 1kiss是什么意思中文
Let R be the region bounded by the graph of 2
stk
2x x y e −= and the
horizontal line and let S be the region bounded by the graph of
2,y =2
2x x y e −= and the horizontal lines and 1y =2,y =
as shown above. (a) Find the area of R . (b) Find the area of S .
本科毕业证查询
(c) Write, but do not evaluate, an integral expression that gives the
volume of the solid generated when R is rotated about the horizontal line 1.y =
2
22x x e −= when 0.446057,1.553943x =Let and 0.446057P = 1.553943Q =
(a) Area of ()
2
220.5Q
x x P
14dx −=−=⌠
⌡⎪⎩R e
3 : ⎪
⎨ 1 : integrand
1 : limits 1 : answer ⎧
(b) when 2
2
21x x e −=0,x =
Area of S e Area of R
()
2
2
20
1x x dx −=−−⌠⌡− Area of
眼霜的用法
2.06016= 1.546R =OR
()
()()
222
220110.219064 1.1078860.219064 1.546
P
x x x x Q
e dx Q P e d −−−+−⋅+−=++=⌠⌠⌡⌡1x
⎪⎩
3 : ⎪
⎨ 1 : integrand 1 : limits 1 : answer ⎧
(c) Volume ()
()22
221
21Q
x x P e d π−⎛
⎞
−−⎜⎟⎝
⎠
⌠⎮⌡x =−
3 : {
2 : integrand
1 : constant and limits
成考查询Question 2
A particle moves along the x -axis so that its velocity v at time
is given by The graph of v is shown above
fallofffor 0t ≥()()
2sin .v t t
=0
t ≤≤ The position of the particle at time t is ()x t and its position at time is 0t =()05x =.
(a) Find the acceleration of the particle at time t 3.=
(b) Find the total distance traveled by the particle from time 0t =
to t 3.==(c) Find the position of the particle at time t 3.
(d) For 0t ≤≤ find the time t at which the particle
is farthest to the right. Explain your answer.
Question 3
The wind chill is the temperature, in degrees Fahrenheit ()F ,° a human feels bad on the air temperature, in degrees Fahrenheit, and the wind velocity v , in miles per hour ()mph . If the air temperature is 32 then the wind chill is given by and is valid for 56F,°()0.1655.622.1W v v =−0.v ≤≤ (a) Find ()20.W ′ Using correct units, explain the meaning of ()20W ′ in terms of the wind chill.
(b) Find the average rate of change of W over the interval 560.v ≤≤ Find the value of v at which the
instantaneous rate of change of W is equal to the average rate of change of W over the interval 560.v ≤≤ (c) Over the time interval hours, the air temperature is a constant 32 At time the wind
velocity is mph. If the wind velocity increas at a constant rate of 5 mph per hour, what is the rate of change of the wind chill with respect to time at 0t ≤≤4 F.°0,t =20v =3t = hours? Indicate units of measure.
Question 4
Let f be a function defined on the clod interval 55x −≤≤ with ()13f
=. The graph of ,f ′ the derivative of f , consists of two micircles and two line gments, as shown above.
(a) For −< find all values x at which f has a
freestyle什么意思relative maximum. Justify your answer.
5x 5,<5,<(b) For −< find all values x at which the graph of f
has a point of inflection. Justify your answer.
南通翻译公司
5x (c) Find all intervals on which the graph of f is concave up
and also has positive slope. Explain your reasoning.
(d) Find the absolute minimum value of ()f x over the clod interval 5x 5.−≤≤ Explain your reasoning.桂林英语培训
