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Deck 3: Section 6: Differentiation
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Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider 
and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find 
when 
. Round your answer to three decimal places. 
A) -17.647 rad/hr
B) 2.941 rad/hr
C) 17.647 rad/hr
D) 0.044 rad/hr
E) -8.824 rad/hr
and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places. A) -17.647 rad/hr
B) 2.941 rad/hr
C) 17.647 rad/hr
D) 0.044 rad/hr
E) -8.824 rad/hr
Question
In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when 
. Round your answer to four decimal places. 
A) -0.6006 rad/sec
B) -0.0581 rad/sec
C) 0.0601 rad/sec
D) 0.0581 rad/sec
E) -0.0601 rad/sec
. Round your answer to four decimal places. A) -0.6006 rad/sec
B) -0.0581 rad/sec
C) 0.0601 rad/sec
D) 0.0581 rad/sec
E) -0.0601 rad/sec
Question
A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of 
with the perpendicular from the light to the wall. 
A)
B)
C)
D)
E)
with the perpendicular from the light to the wall. A)
B)
C)
D)
E)
Question
Find the slope-intercept form of the equation of the line tangent to the graph of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find 
at the point 
for the equation 
.
A)
B)
C)
D)
E)
at the point for the equation .A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. At what time will the object reach the ground level? 
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
Question
An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider 
and x as shown in the following figure. Write 
as a function of x. 
A)
B)
C)
D)
E)
and x as shown in the following figure. Write as a function of x. A)
B)
C)
D)
E)
Question
Find 
at the point 
for the equation 
.
A)
B)
C)
D)
E)
at the point for the equation .A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write 
as a function of x. 
A)
B)
C)
D)
E)
as a function of x. A)
B)
C)
D)
E)
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Deck 3: Section 6: Differentiation
1
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
2
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
3
An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places.
A) -17.647 rad/hr
B) 2.941 rad/hr
C) 17.647 rad/hr
D) 0.044 rad/hr
E) -8.824 rad/hr
and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places. A) -17.647 rad/hr
B) 2.941 rad/hr
C) 17.647 rad/hr
D) 0.044 rad/hr
E) -8.824 rad/hr
17.647 rad/hr
4
In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places.
A) -0.6006 rad/sec
B) -0.0581 rad/sec
C) 0.0601 rad/sec
D) 0.0581 rad/sec
E) -0.0601 rad/sec
. Round your answer to four decimal places. A) -0.6006 rad/sec
B) -0.0581 rad/sec
C) 0.0601 rad/sec
D) 0.0581 rad/sec
E) -0.0601 rad/sec
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5
A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.
A)
B)
C)
D)
E)
with the perpendicular from the light to the wall. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
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k this deck
6
Find the slope-intercept form of the equation of the line tangent to the graph of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock for access to all 16 flashcards in this deck.
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7
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock for access to all 16 flashcards in this deck.
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8
Find at the point for the equation .
A)
B)
C)
D)
E)
at the point for the equation .A)
B)
C)
D)
E)
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9
Find an equation of the tangent line to the graph of at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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Unlock for access to all 16 flashcards in this deck.
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10
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
11
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
12
In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. At what time will the object reach the ground level?
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
A) 3 seconds
B) 6 seconds
C) 7 seconds
D) 5 seconds
E) 4 seconds
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Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
13
An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider and x as shown in the following figure. Write as a function of x.
A)
B)
C)
D)
E)
and x as shown in the following figure. Write as a function of x. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
14
Find at the point for the equation .
A)
B)
C)
D)
E)
at the point for the equation .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
15
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
16
A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write as a function of x.
A)
B)
C)
D)
E)
as a function of x. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
