تكلم مع الذكاء الاصطناعي
Deck 13: Section 7: Functions of Several Variables
ملء الشاشة (f)
سؤال
Find 
for function 
.
A)
B)
C)
D)
E)
for function .A)
B)
C)
D)
E)
سؤال
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)
سؤال
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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
. سؤال
Find the directional derivative of the function at P in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
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
سؤال
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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)
سؤال
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
. سؤال
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)
سؤال
Find the directional derivative of the function in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
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/
سؤال
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)
سؤال
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)
سؤال
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 سؤال
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)
سؤال
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
سؤال
Find the gradient of the function at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the directional derivative of the function at P in the direction of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
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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العب
ملء الشاشة (f)
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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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
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7
Find the gradient of the function at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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)
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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
. فتح الحزمة
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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)
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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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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/
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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)
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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)
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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 فتح الحزمة
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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)
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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
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 20 في هذه المجموعة.
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18
Find the gradient of the function at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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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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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
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