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Review of Calculus AB
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Review of Calculus AB
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Table of Contents
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Full Book Quiz
1. Compute
.
0
The limit does not exist.
8
∞
2. Compute
.
8
The limit does not exist.
∞
0
3. What type of function is
f
(
x
) =
x
^{6}
?
Even
Odd
Neither
f
is not a function.
4. What type of function is
f
(
x
) =
x
^{3}
+ 3
x
?
Even
Odd
Neither
f
is not a function.
5. What type of function is
f
(
x
) =
x
?
Even
Odd
Neither
f
is not a function.
6. For the following function, what value must be assigned to
f
(3)
to make the function continuous at
x
= 3
?
f
(
x
) =
Any value will correct the discontinuity.
No value will correct the discontinuity.
8
7
7. A general expression for the derivative of
f
(
x
)
is:
8. What is the derivative of
f
(
x
) =
Π
^{4}
?
Π
^{3}
0
x
^{3}
9. What is the derivative of
f
(
x
) =
sin
?

cos

sin

cos
cos

cos
+
sin
10. What is the derivative of
f
(
x
) =
?
3
x
^{2}
tan(
x
)
11. For the function
f
(
x
) =
x
^{2}
 4
x
+ 5
, give the equation of the tangent at
x
= 3
.
y
=
x
^{2}
 4
x
+ 3
y
=
x
^{3}
2
x
^{2}
+ 5
x
+
c
y
= 
x
+
y
= 2
x
 4
12. Find the equation of the line normal to the tangent of
f
(
x
) =
x
^{2}
 4
x
+ 5
at
x
= 1
.
y
=
x
^{2}
 4
x
+ 3
y
=
x
^{3}
2
x
^{2}
+ 5
x
+
c
y
=
x
+ 1
y
= 2
x
 4
13. Compute
where
x
= 4
x
^{2}
y
 2
y
.
8
xy
 2
8
xy
 2
y
14. Car A and Car B start at the same point. At time
t
= 0
, Car A travels south at 40 miles per hour. Car B travels west at 20 miles per hour. At what rate is the distance between the two cars changing at
t
= 3
hours?
60
mph
50.38
mph
40
mph
44.72
mph
15. The momentum of an object is given by the relation
p
=
mv
, where
m
=mass and
v
=velocity. If an object weighing
3
kg accelerates at
2
m
/
s
^{2}
, what is the rate of change of its momentum?
4
6
8
12
16. The position of an object is represented by
s
(
t
) =
t
^{2}

t
 1
. What is the object's velocity at
t
= 3
seconds?
1
m/s
3
m/s
5
m/s
6
m/s
17. If the position of an object is represented by the equation
s
(
t
) =
t
^{2}

t
 1
, what is the total distance traveled between
t
= 0
and
t
= 2
?
2
m
2.5
m
3
m
5
m
18. Find a number
c
on
[
a
,
b
]
such that
f'
(
c
) =
where
f
(
x
) = 2
x
^{2}
and
[
a
,
b
] = [ 1, 2]

1
1
19. For the function
f
(
x
) =
x
^{3}
, is the critical point at
x
= 0
a local maximum, local minimum or neither?
Local maximum
Local minimum
Both a local maximum and a local minimum
Neither a local maximum nor a local minimum
20. Find the inflection points on the interval
[
,
]
for the function
f
(
x
) = sin(
x
)
.
x
= 0,
, 2
x
= 
,
,
Π
x
= 0,
Π
, 2
x
= 0,
Π
,
21. Does
f
(
x
) =
have a horizontal asymptote?
No.
Yes, at
y
= 3/4
.
Yes, at
y
= 5
.
Yes, at
∞
.
22. Sophia is standing
1000
feet away from the base of a tall building. At time
t
= 0
, she sees a baby drop from the roof of that building and calculates that it will hit the ground in
21
seconds. Her normal running speed is
10
feet per second, but she can increase her speed by
10
feet per second with each apple she eats. If it takes her one second to eat an apple, how many apples should she eat in order to minimize the total time it will take (eating + running) to get to the base of the building?
7 apples
8 apples
9 apples
10 apples
23. A triangle has two sides that are each 5 cm long. What angle between the two sides will maximize the triangle's area?
24. Let
F
(
x
) =
x
^{4}
 2
x
. What kind of point occurs at
x
= 3
?
Local minimum
Local maximum
Neither a local minimum nor a local maximum
The function is undefined at that point
25. What is the derivative of
f
(
x
) =
?
1 +
1 
26. Evaluate
7
dx
.
7
7 +
c
7
x
7
x
+
c
27. Evaluate
sin(7
x
+17)
dx
.

cos(7
x
+ 17) +
c
cos(7
x
+ 17) +
c

sin(7
x
+ 17) +
c
sin(7
x
+ 17) +
c
28.
Evaluate
cos(
Π

x
)
dx
.
sin(
Π

x
) +
c
sin(
Π

x
) +
c
Π
sin(
Π

x
) +
c
cos(
Π

x
) +
c
29. Evaluate
t
dt
(
t
^{2}
8)
^{}
+
c
2
t
(
t
^{2}
8)
^{}
+
c
(
t
^{2}
8)
^{}
+
c
(
t
^{2}
8)
^{}
+
c
30. Using left endpoints and 4 rectangles, approximate
x
^{2}
dx
.
24
26
32
48
31. Using right endpoints and 4 rectangles, approximate
x
^{2}
dx
.
26
35
43
49
32. Evaluate
x
^{2}
sin
dx
.
0
1
8
Π
16/
pi
33. Evaluate
sin(
x
)
dx
.

0
34. The velocity of a particle is given by the equation
v
(
t
) =
t
^{3}
 2
. What is the total change in position from
t
= 0
to
t
= 2
?
0
2
4
8
35. What is the average value of
f
(
x
) = 11
x
^{2}
 2
on [1,1]?
0
5/3
8/3
3
36. What is the average value of
f
(
x
) =
on
[0, 2
Π
]
?
Π
1
1/2
0
37. Compute
sin(
t
^{4}
)
dt
.
sin(
x
^{4}
)
cos(
x
^{4}
)
cos(
x
^{4}
)
cos(
t
^{4}
)
38. Evaluate
cos(
t
+4)
dt
.
sin(
t
+ 4)
cos(
t
+ 4)
cos(
x
+ 4)
sin(
x
+ 4)
39. Using 4 trapezoids, approximate
x
^{2}
dx
.
10
30
50
70
40. If
f
(
x
) =
x
^{3}
, compute
f
^{1}
(2)
.
41. Evaluate
Π
^{x}
.
Π
^{x}
ln
Π
Πx
^{Π1}
x
^{x}
1+ln
x
0
42. Evaluate
x
^{Π}
.
Π
^{x}
ln
Π
Πx
^{Π1}
x
^{x}
1+ln
x
0
43. Evaluate
x
^{x}
.
Π
^{x}
ln
Π
Πx
^{Π1}
x
^{x}
1+ln
x
0
44. What is the rate constant of a substance that decays 27\% after 20 minutes?
45. If
= 7
y
, what is a possible equation for the corresponding function?
y
= 7
e
^{7t}
y
=
e
^{7t}
y
=
e
^{7t}
y
=
e
^{t}
46. Evaluate
log
_{3}
3
^{87}
.
27
87
131
47. Evaluate
dx
.
1
e
e
^{2}
48. Evaluate
e
^{3x}
dx
.
e
^{3x}
e
^{x}
e
^{3x}
3
e
^{3x}
49. Evaluate
log
_{7}
(56)  log
_{7}
(8)
.
Does not exist
1
7
10
50. Evaluate
7
^{x}
dx
.
x
7
^{x1}
+
c
7
^{x1}
+
c
7
^{x}
+
c
7
^{x}
+
c
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