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Deck 13: Section 7: Functions of Several Variables
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Question
Find 
for function 
.
A)
B)
C)
D)
E)
for function .A)
B)
C)
D)
E)
Question
The surface of a mountain is modeled by the equation 
. A mountain climber is at the point 
. In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.
A)
B)
C)
D)
E)
. A mountain climber is at the point . In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.A)
B)
C)
D)
E)
Question
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The temperature at the point 
on a metal plate is modeled by 
, 
. Find the directions of no change in heat on the plate from the point 
.
A) There will be no change in directions perpendicular to the gradient
.
B) There will be no change in directions parallel to the gradient
.
C) There will be no change in directions parallel to the gradient
.
D) There will be no change in directions perpendicular to the gradient
.
E) There will be no change in directions perpendicular to the gradient
.
on a metal plate is modeled by , . Find the directions of no change in heat on the plate from the point .A) There will be no change in directions perpendicular to the gradient
.B) There will be no change in directions parallel to the gradient
.C) There will be no change in directions parallel to the gradient
.D) There will be no change in directions perpendicular to the gradient
.E) There will be no change in directions perpendicular to the gradient
. Question
Find the directional derivative of the function at P in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the directional derivative of the function 
at 
in the direction of 
. Round your answer to two decimal places.
A) -11.64
B) -1.87
C) -5.86
D) -0.70
E) -5.62
at in the direction of . Round your answer to two decimal places.A) -11.64
B) -1.87
C) -5.86
D) -0.70
E) -5.62
Question
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the gradient to find a normal vector to the graph of the equation at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The temperature at the point 
on a metal plate is modeled by 
, 
. Find the direction of greatest increase in heat from the point 
.
A) The greatest increase is in the direction of the gradient
.
B) The greatest increase is in the direction of the gradient
.
C) The greatest increase is in the direction of the gradient
.
D) The greatest increase is in the direction of the gradient
.
E) The greatest increase is in the direction of the gradient
.
on a metal plate is modeled by , . Find the direction of greatest increase in heat from the point .A) The greatest increase is in the direction of the gradient
.B) The greatest increase is in the direction of the gradient
.C) The greatest increase is in the direction of the gradient
.D) The greatest increase is in the direction of the gradient
.E) The greatest increase is in the direction of the gradient
. Question
The temperature at the point 
on a metal plate is 
. Find the direction of greatest increase in heat from the point 
. Round all numerical values in your answer to three decimal places.
A)
B)
C)
D)
E)
on a metal plate is . Find the direction of greatest increase in heat from the point . Round all numerical values in your answer to three decimal places.A)
B)
C)
D)
E)
Question
Find the directional derivative of the function in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the directional derivative of the function at P in the direction of 
. 
A) 4/
B) -8/
C) 12/
D) 24/
E) -24/
. A) 4/
B) -8/
C) 12/
D) 24/
E) -24/
Question
Find the path of a heat-seeking particle placed at point 
on a metal plate with a temperature field 
.
A)
B)
C)
D)
E)
on a metal plate with a temperature field .A)
B)
C)
D)
E)
Question
Use the gradient to find the directional derivative of the function at P in the direction of Q. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
For function 
, find the maximum value of the directional derivative at (3,2).
A)
/8
B)
/56
C)
/224
D)
/112
E)
/168
, find the maximum value of the directional derivative at (3,2).A)
/8B)
/56C)
/224D)
/112E)
/168 Question
Use the gradient to find the directional derivative of the function at P in the direction of Q. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the maximum value of the directional derivative at the point 
of the function 
. Round your answer to two decimal places.
A) 899.28
B) 814.59
C) 922.05
D) 933.23
E) 538.80
of the function . Round your answer to two decimal places.A) 899.28
B) 814.59
C) 922.05
D) 933.23
E) 538.80
Question
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the directional derivative of the function at P in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the maximum value of the directional derivative at the point 
of the function 
. Round your answer to two decimal places.
A) 0.55
B) 0.14
C) 0.56
D) 0.10
E) 0.06
of the function . Round your answer to two decimal places.A) 0.55
B) 0.14
C) 0.56
D) 0.10
E) 0.06
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Deck 13: Section 7: Functions of Several Variables
1
Find for function .
A)
B)
C)
D)
E)
for function .A)
B)
C)
D)
E)
2
The surface of a mountain is modeled by the equation . A mountain climber is at the point . In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.
A)
B)
C)
D)
E)
. A mountain climber is at the point . In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.A)
B)
C)
D)
E)
3
Find the gradient of the function at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
The temperature at the point on a metal plate is modeled by , . Find the directions of no change in heat on the plate from the point .
A) There will be no change in directions perpendicular to the gradient .
B) There will be no change in directions parallel to the gradient .
C) There will be no change in directions parallel to the gradient .
D) There will be no change in directions perpendicular to the gradient .
E) There will be no change in directions perpendicular to the gradient .
on a metal plate is modeled by , . Find the directions of no change in heat on the plate from the point .A) There will be no change in directions perpendicular to the gradient
.B) There will be no change in directions parallel to the gradient
.C) There will be no change in directions parallel to the gradient
.D) There will be no change in directions perpendicular to the gradient
.E) There will be no change in directions perpendicular to the gradient
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5
Find the directional derivative of the function at P in the direction of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
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6
Find the directional derivative of the function at in the direction of . Round your answer to two decimal places.
A) -11.64
B) -1.87
C) -5.86
D) -0.70
E) -5.62
at in the direction of . Round your answer to two decimal places.A) -11.64
B) -1.87
C) -5.86
D) -0.70
E) -5.62
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
7
Find the gradient of the function at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
8
Use the gradient to find a normal vector to the graph of the equation at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
9
The temperature at the point on a metal plate is modeled by , . Find the direction of greatest increase in heat from the point .
A) The greatest increase is in the direction of the gradient .
B) The greatest increase is in the direction of the gradient .
C) The greatest increase is in the direction of the gradient .
D) The greatest increase is in the direction of the gradient .
E) The greatest increase is in the direction of the gradient .
on a metal plate is modeled by , . Find the direction of greatest increase in heat from the point .A) The greatest increase is in the direction of the gradient
.B) The greatest increase is in the direction of the gradient
.C) The greatest increase is in the direction of the gradient
.D) The greatest increase is in the direction of the gradient
.E) The greatest increase is in the direction of the gradient
. Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
10
The temperature at the point on a metal plate is . Find the direction of greatest increase in heat from the point . Round all numerical values in your answer to three decimal places.
A)
B)
C)
D)
E)
on a metal plate is . Find the direction of greatest increase in heat from the point . Round all numerical values in your answer to three decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
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11
Find the directional derivative of the function in the direction of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
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12
Find the directional derivative of the function at P in the direction of .
A) 4/
B) -8/
C) 12/
D) 24/
E) -24/
. A) 4/
B) -8/
C) 12/
D) 24/
E) -24/
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
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13
Find the path of a heat-seeking particle placed at point on a metal plate with a temperature field .
A)
B)
C)
D)
E)
on a metal plate with a temperature field .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
14
Use the gradient to find the directional derivative of the function at P in the direction of Q.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
15
For function , find the maximum value of the directional derivative at (3,2).
A) /8
B) /56
C) /224
D) /112
E) /168
, find the maximum value of the directional derivative at (3,2).A)
/8B)
/56C)
/224D)
/112E)
/168 Unlock Deck
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Unlock Deck
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16
Use the gradient to find the directional derivative of the function at P in the direction of Q.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
17
Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.
A) 899.28
B) 814.59
C) 922.05
D) 933.23
E) 538.80
of the function . Round your answer to two decimal places.A) 899.28
B) 814.59
C) 922.05
D) 933.23
E) 538.80
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
18
Find the gradient of the function at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
19
Find the directional derivative of the function at P in the direction of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
20
Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.
A) 0.55
B) 0.14
C) 0.56
D) 0.10
E) 0.06
of the function . Round your answer to two decimal places.A) 0.55
B) 0.14
C) 0.56
D) 0.10
E) 0.06
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
