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Deck 4: Section 8: Applications of Differentiation
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Question
The measurements of the base and altitude of a triangle are found to be 54 and 33 centimeters. The possible error in each measurement is 0.25 centimeter. Use differentials to estimate the propagated error in computing the area of the triangle. Round your answer to four decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Compare dy and 
for 
at x = 0 with 
Give your answers to four decimal places.
A)
B)
C)
D)
E)
for at x = 0 with Give your answers to four decimal places.A)
B)
C)
D)
E)
Question
The radius of a spherical balloon is measured to be 12 inches, with a possible error of 0.06 inch. Use differentials to approximate the maximum possible error in calculating the surface area of the sphere. Round your answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the differential dy of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the equation of the tangent line T to the graph of 
at the given point 
A)
B)
C)
D)
E)
at the given point A)
B)
C)
D)
E)
Question
Find the equation of the tangent line T to the graph of 
at the given point 
A)
B)
C)
D)
E)
at the given point A)
B)
C)
D)
E)
Question
The range R of a projectile is 
where 
is the initial velocity in feet per second and 
is the angle of elevation. If 
feet per second and 
is changed from 
to 
use differentials to approximate the change in the range. Round your answer to the nearest integer.
A) 2,593 ft
B) 4,568 ft
C) 5,623 ft
D) 2,811 ft
E) 5,186 ft
where is the initial velocity in feet per second and is the angle of elevation. If feet per second and is changed from to use differentials to approximate the change in the range. Round your answer to the nearest integer.A) 2,593 ft
B) 4,568 ft
C) 5,623 ft
D) 2,811 ft
E) 5,186 ft
Question
Find the differential dy of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the differential dy of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of 
inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.
A)
B)
C)
D)
E)
inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.A)
B)
C)
D)
E)
Question
Use differentials to approximate the value of 
. Round your answer to four decimal places.
A) 5.0000
B) 5.0100
C) 5.0400
D) 5.0200
E) 5.0300
. Round your answer to four decimal places.A) 5.0000
B) 5.0100
C) 5.0400
D) 5.0200
E) 5.0300
Question
The total stopping distance T of a vehicle is 
where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from 
to 
miles per hour. Round your answer to one decimal place.
A) 37.4%
B) 16.5%
C) 32.2%
D) 168.0%
E) 116.7%
where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from to miles per hour. Round your answer to one decimal place.A) 37.4%
B) 16.5%
C) 32.2%
D) 168.0%
E) 116.7%
Question
The radius of a spherical balloon is measured to be 8 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the volume of the sphere. Round your answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use differentials to approximate the value of 
. Round your answer to four decimal places.
A) 1.9683
B) 1.9483
C) 1.9383
D) 1.9583
E) 1.9783
. Round your answer to four decimal places.A) 1.9683
B) 1.9483
C) 1.9383
D) 1.9583
E) 1.9783
Question
The measurement of the side of a square floor tile is 14 inches, with a possible error of 
inch. Use differentials to approximate the possible propagated error in computing the area of the square.
A)
B)
C)
D)
E)
inch. Use differentials to approximate the possible propagated error in computing the area of the square.A)
B)
C)
D)
E)
Question
Compare dy and 
for 
at x = -1 with 
Give your answers to four decimal places.
A)
B)
C)
D)
E)
for at x = -1 with Give your answers to four decimal places.A)
B)
C)
D)
E)
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Deck 4: Section 8: Applications of Differentiation
1
The measurements of the base and altitude of a triangle are found to be 54 and 33 centimeters. The possible error in each measurement is 0.25 centimeter. Use differentials to estimate the propagated error in computing the area of the triangle. Round your answer to four decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Compare dy and for at x = 0 with Give your answers to four decimal places.
A)
B)
C)
D)
E)
for at x = 0 with Give your answers to four decimal places.A)
B)
C)
D)
E)
3
The radius of a spherical balloon is measured to be 12 inches, with a possible error of 0.06 inch. Use differentials to approximate the maximum possible error in calculating the surface area of the sphere. Round your answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find the differential dy of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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5
Find the equation of the tangent line T to the graph of at the given point
A)
B)
C)
D)
E)
at the given point A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
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6
Find the equation of the tangent line T to the graph of at the given point
A)
B)
C)
D)
E)
at the given point A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
7
The range R of a projectile is where is the initial velocity in feet per second and is the angle of elevation. If feet per second and is changed from to use differentials to approximate the change in the range. Round your answer to the nearest integer.
A) 2,593 ft
B) 4,568 ft
C) 5,623 ft
D) 2,811 ft
E) 5,186 ft
where is the initial velocity in feet per second and is the angle of elevation. If feet per second and is changed from to use differentials to approximate the change in the range. Round your answer to the nearest integer.A) 2,593 ft
B) 4,568 ft
C) 5,623 ft
D) 2,811 ft
E) 5,186 ft
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
8
Find the differential dy 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
9
Find the differential dy 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
10
The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.
A)
B)
C)
D)
E)
inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
11
Use differentials to approximate the value of . Round your answer to four decimal places.
A) 5.0000
B) 5.0100
C) 5.0400
D) 5.0200
E) 5.0300
. Round your answer to four decimal places.A) 5.0000
B) 5.0100
C) 5.0400
D) 5.0200
E) 5.0300
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
12
The total stopping distance T of a vehicle is where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from to miles per hour. Round your answer to one decimal place.
A) 37.4%
B) 16.5%
C) 32.2%
D) 168.0%
E) 116.7%
where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from to miles per hour. Round your answer to one decimal place.A) 37.4%
B) 16.5%
C) 32.2%
D) 168.0%
E) 116.7%
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
13
The radius of a spherical balloon is measured to be 8 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the volume of the sphere. Round your answer to two decimal places.
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
14
Use differentials to approximate the value of . Round your answer to four decimal places.
A) 1.9683
B) 1.9483
C) 1.9383
D) 1.9583
E) 1.9783
. Round your answer to four decimal places.A) 1.9683
B) 1.9483
C) 1.9383
D) 1.9583
E) 1.9783
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
15
The measurement of the side of a square floor tile is 14 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the square.
A)
B)
C)
D)
E)
inch. Use differentials to approximate the possible propagated error in computing the area of the square.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
16
Compare dy and for at x = -1 with Give your answers to four decimal places.
A)
B)
C)
D)
E)
for at x = -1 with Give your answers to four decimal places.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.
