تكلم مع الذكاء الاصطناعي
Deck 8: Calculus of Several Variables
ملء الشاشة (f)
سؤال
Find the volume of the solid bounded above by the surface 
and below by the plane region R. 
; R is the region bounded by 
.
and below by the plane region R. ; R is the region bounded by .
سؤال
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function 
Where
stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies betweenand 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per week
B)
per week
C)
per week
D)
per week
E)
per week
Where
stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies betweenand 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per weekB)
per weekC)
per weekD)
per weekE)
per week سؤال
Find the average value of the given function 
over the plane region R. 
; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A) 
B) 
C) 
D) 
E) 
over the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid bounded above by the surfac 
and below by the plane region R. 
; R is the triangle with vertices (0, 0), (2, 0) and (0, 2).
and below by the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (0, 2). سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A) 36
B) 24
C) 144
D) 12
E) 48
A) 36
B) 24
C) 144
D) 12
E) 48
سؤال
Find the volume of the solid bounded above by the surface 
and below by the plane region R. 
and R is the region bounded by the graphs of 
.
A)
B) 
C) 
D) 
E) 
and below by the plane region R. and R is the region bounded by the graphs of .
A)
B)
C)
D)
E)
سؤال
Use a double integral to find the volume of the solid shown in the figure.
__________ cu units.
__________ cu units.
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A)
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid bounded above by the surface 
and below by the plane region R. 
and R is the region bounded by the graphs of 
and 
.
and below by the plane region R. and R is the region bounded by the graphs of and . سؤال
The population density of a certain city is given by the function 
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B) 
C) 
D) 
E) 
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
E)
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A)
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
Find the average value of the function 
over the plane region R. 
and R is the triangle with vertices 
, 
and 
.
A) 5
B) 
C) 25
D) 
E)
over the plane region R. and R is the triangle with vertices , and . A) 5
B)
C) 25
D)
E)
سؤال
Find the volume of the solid bounded above by the surface 
And below by the plane region R.
R is the triangle with vertices
and 
.
A)
B) 
C) 
D) 
E) 
And below by the plane region R.
R is the triangle with vertices
and .
A)
B)
C)
D)
E)
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A) 12
B) 96
C) 64
D) 256
E) 384
A) 12
B) 96
C) 64
D) 256
E) 384
سؤال
Find the volume of the solid bounded above by the surface 
and below by the plane region R. 
; R is the region bounded by 
.
A)
B) 
C) 
D) 
E) 
and below by the plane region R. ; R is the region bounded by .
A)
B)
C)
D)
E)
سؤال
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
سؤال
Use a double integral to find the volume of the solid shown in the figure.
__________ cu units.
__________ cu units.
سؤال
Find the average value of the given function 
over the plane region R. 
; R is the region bounded by the graph of 
and 
from 
to 
.
A)
B) 
C) 
D) 
E) 
over the plane region R. ; R is the region bounded by the graph of and from to .
A)
B)
C)
D)
E)
سؤال
Use a double integral to find the volume of the solid shown in the figure.
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
F(x, y) = 6x + 6y; R is bounded by x = 0,
, y = 0 and y = 4.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 6x + 6y; R is bounded by x = 0,
, y = 0 and y = 4.
A)
B)
C)
D)
سؤال
Find the volume of the solid bounded above by the surface
Z = f(x, y)
And below by the plane region R.
; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).
A)
B)
C)
Z = f(x, y)
And below by the plane region R.
; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).
A)
B)
C)
سؤال
Evaluate the double integral 
For the function
and the region R.
and R is the rectangle defined by 
and 
.
A) 8
B) 6
C) 2
D) 3
E) 5
For the function
and the region R.
and R is the rectangle defined by and .
A) 8
B) 6
C) 2
D) 3
E) 5
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
F(x, y) = 4x + 2y; R is bounded by x = 0, x = 4, y = 0 and y = x.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 4x + 2y; R is bounded by x = 0, x = 4, y = 0 and y = x.
A)
B)
C)
D)
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
; R is the rectangle defined by 
and 
.
A) 0
B) 4
C) -4
D) 1
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) 0
B) 4
C) -4
D) 1
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
; R is bounded by 
and y = x.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
; R is bounded by and y = x.
A)
B)
C)
D)
سؤال
Find the average value of the given function 
over the plane region R.
; R is the triangle with vertices (0, 0), (1, 0) and (1, 1).
over the plane region R.
; R is the triangle with vertices (0, 0), (1, 0) and (1, 1). سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
F(x, y) = 2y + x; R is the rectangle defined by
and 
.
A)
B)
C)
D) 26
For the given function f(x, y) and the region R.
F(x, y) = 2y + x; R is the rectangle defined by
and .
A)
B)
C)
D) 26
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A) 6
B) 4
C) 9
D) 14
A) 6
B) 4
C) 9
D) 14
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
A) 2.5
B) 3.5e
C) -3.5
D) -2.5
For the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
A) 2.5
B) 3.5e
C) -3.5
D) -2.5
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
F(x, y) = 6x + 12y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 6x + 12y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
A)
B)
C)
D)
سؤال
Find the average value of the given function 
over the plane region R.
; R is the region bounded by the graph of 
and 
from 
to 
.
over the plane region R.
; R is the region bounded by the graph of and from to . سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
; R is the rectangle defined by 
and 
A)
B)
C)
D)
For the given function f(x, y) and the region R.
; R is the rectangle defined by and A)
B)
C)
D)
سؤال
Find the volume of the solid bounded above by the surface
Z = f(x, y)
And below by the plane region R.
; R is the region bounded by 
, 
, and 
.
A)
B)
C)
Z = f(x, y)
And below by the plane region R.
; R is the region bounded by , , and .
A)
B)
C)
سؤال
Evaluate the double integral 
For the function
and the region R.
and R is bounded by 
, 
, 
and 
.
A)
B)
C)
D)
E)
For the function
and the region R.
and R is bounded by , , and .
A)
B)
C)
D)
E)
سؤال
Evaluate the double integral 
For the given function f(x, y) and the region R.
; R is the rectangle defined by 
and 
.
A) -10
B) 10e
C) 9
D) -9e
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) -10
B) 10e
C) 9
D) -9e
سؤال
Use a double integral to find the volume of the solid shown in the figure. 
A) 5,996
B) 6,008
C) 6,000
D) 5,994
A) 5,996
B) 6,008
C) 6,000
D) 5,994
سؤال
Find the average value of the function 
over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1). سؤال
Find the volume of the solid bounded above by the surface 
And below by the plane region R.
and R is the region bounded by the graphs of 
and 
.
A)
B)
C)
D)
E)
And below by the plane region R.
and R is the region bounded by the graphs of and .
A)
B)
C)
D)
E)
سؤال
Evaluate the double integral 
for the given function f(x, y) and the region R. Enter your answer as a fraction. 
; R is the rectangle defined by 
and 
.
for the given function f(x, y) and the region R. Enter your answer as a fraction. ; R is the rectangle defined by and . سؤال
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function 
Where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per week
B)
per week
C)
per week
D)
per week
E)
per week
Where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per weekB)
per weekC)
per weekD)
per weekE)
per week سؤال
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_6725_b0a1_abb0ce5e996b_TB8255_11.jpg)
where ![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_6726_b0a1_05e29c894151_TB8255_11.jpg)
.
A) From the definition follows![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_6727_b0a1_2b5f95c919b1_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e38_b0a1_93acc4ae3fb9_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e39_b0a1_01db2b4e5c74_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3a_b0a1_e99c7fc18596_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3b_b0a1_c100a560b7f6_TB8255_11.jpg)
, so the statement is false.
B) From the definition follows![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3c_b0a1_3b81855ebcad_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3d_b0a1_9f958824f5c9_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3e_b0a1_e5aea5cc6ad2_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e3f_b0a1_b9cefa9d035c_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_8e40_b0a1_bf28c28213bb_TB8255_11.jpg)
, so the statement is true.
C) From the definition follows![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_b551_b0a1_6deebf5c8047_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_b552_b0a1_0d06b43c908a_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_b553_b0a1_f57b73363d8b_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_b554_b0a1_153e0fa2a49d_TB8255_11.jpg)
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where . </strong> A) From the definition follows , so the statement is false. B) From the definition follows , so the statement is true. C) From the definition follows , so the statement is false. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cadb_b555_b0a1_b94a8229bff6_TB8255_11.jpg)
, so the statement is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where .
A) From the definition follows
, so the statement is false.B) From the definition follows
, so the statement is true.C) From the definition follows
, so the statement is false. سؤال
Use a double integral to find the volume of the solid shown in the figure.
سؤال
Find the average value of the function 
Over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
A)
B)
C)
D)
E)
Over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
A)
B)
C)
D)
E)
سؤال
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
سؤال
Evaluate the double integral
for the given function f(x, y) and the region R. Enter your answer as a fraction.
f(x, y) = 0x + 0y; R is bounded by x = 0,
, y = 0 and y = 4.
for the given function f(x, y) and the region R. Enter your answer as a fraction.
f(x, y) = 0x + 0y; R is bounded by x = 0,
, y = 0 and y = 4. سؤال
Evaluate the double integral
for the function
and the region R.
and R is the rectangle defined by 
and 
.
for the function
and the region R.
and R is the rectangle defined by and . سؤال
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is the rectangle defined by 
and 
.
for the given function f(x, y) and the region R.
; R is the rectangle defined by and . سؤال
Evaluate the double integral 
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 2y + 3x; R is the rectangle defined by 
and 
.
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 2y + 3x; R is the rectangle defined by and . سؤال
Find the average value of the given function 
Over the plane region R.
; R is the region bounded by the graph of y = 8x and y = 0 from x = 1 to x = 7.
A)
B)
C)
D)
Over the plane region R.
; R is the region bounded by the graph of y = 8x and y = 0 from x = 1 to x = 7.
A)
B)
C)
D)
سؤال
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
for the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x. سؤال
Evaluate the double integral 
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x.
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x. سؤال
Use a double integral to find the volume of the solid shown in the figure.
سؤال
The population density of a certain city is given by the function 
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
سؤال
Evaluate the double integral 
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 4x + 8y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 4x + 8y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1. سؤال
Find the average value of the given function
F(x, y)
Over the plane region R.
; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
F(x, y)
Over the plane region R.
; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
سؤال
Evaluate the double integral
for the function
and the region R. Enter your answer as an expression.
and R is bounded by 
, 
, 
and 
.
for the function
and the region R. Enter your answer as an expression.
and R is bounded by , , and . سؤال
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is the rectangle defined by 
and 
.
for the given function f(x, y) and the region R.
; R is the rectangle defined by and . سؤال
Find the total differential of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the total differential of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the approximate change in z when the point 
changes from 
to 
. 
; from 
to 
A) 
B) 
C) 
D) 
E)
changes from to . ; from to A)
B)
C)
D)
E)
سؤال
Find the average value of the given function
f(x, y)
over the plane region R. Enter your answer as a fraction.
; R is the triangle with vertices (0, 0), (5, 0) and (5, 5).
f(x, y)
over the plane region R. Enter your answer as a fraction.
; R is the triangle with vertices (0, 0), (5, 0) and (5, 5). سؤال
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid bounded above by the surface
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the region bounded by 
, 
and 
.
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the region bounded by , and . سؤال
Find the volume of the solid bounded above by the surface
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the triangle with vertices (0, 0), (4, 0) and (0, 4).
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the triangle with vertices (0, 0), (4, 0) and (0, 4). سؤال
Use a double integral to find the volume of the solid shown in the figure. Enter your answer as an expression.
سؤال
Find the total differential of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
![Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where .<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cade_26a1_b0a1_652ca1a399ab_TB8255_11.jpg)
where ![Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where .<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB8255/11eb651f_cade_26a2_b0a1_bd6e5e1559fb_TB8255_11.jpg)
.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where . سؤال
Find the approximate change in z when the point 
changes from 
to 
. 
; from 
to 
A) 
B) 
C) 
D) 
E)
changes from to . ; from to A)
B)
C)
D)
E)
سؤال
Find the approximate change in z when the point 
changes from 
to 
. 
; from 
to 
A) 
B)
C) 
D) 
E) 
changes from to . ; from to A)
B)
C)
D)
E)
سؤال
Evaluate the double integral
for the given function f(x, y) and the region R. Enter your answer as an expression.
; R is bounded by 
and y = x.
for the given function f(x, y) and the region R. Enter your answer as an expression.
; R is bounded by and y = x. سؤال
Find the average value of the given function
f(x, y)
over the plane region R. Enter your answer as an expression.
; R is the region bounded by the graph of y = 2x and y = 0 from x = 1 to x = 7.
f(x, y)
over the plane region R. Enter your answer as an expression.
; R is the region bounded by the graph of y = 2x and y = 0 from x = 1 to x = 7. سؤال
Use a double integral to find the volume of the solid shown in the figure. Enter your answer as a formula.
سؤال
Find the total differential of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the total differential of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the average value of the function
over the plane region R. Enter your answer as an expression.
and R is the triangle with vertices 
, 
and 
.
over the plane region R. Enter your answer as an expression.
and R is the triangle with vertices , and . سؤال
Find the volume of the solid bounded above by the surface
and below by the plane region R. Enter your answer as a formula.
and R is the region bounded by the graphs of 
and 
.
and below by the plane region R. Enter your answer as a formula.
and R is the region bounded by the graphs of and . سؤال
The population density of a certain city is given by the function
where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
. Enter your answer as an expression.
where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
. Enter your answer as an expression.
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العب
ملء الشاشة (f)
Deck 8: Calculus of Several Variables
1
Find the volume of the solid bounded above by the surface and below by the plane region R. ; R is the region bounded by .
and below by the plane region R. ; R is the region bounded by .
2
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
Where stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies betweenand 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A) per week
B) per week
C) per week
D) per week
E) per week
Where
stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies betweenand 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per weekB)
per weekC)
per weekD)
per weekE)
per week per week 3
Find the average value of the given function over the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
E)
over the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
E)
4
Find the volume of the solid bounded above by the surfac and below by the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (0, 2).
and below by the plane region R. ; R is the triangle with vertices (0, 0), (2, 0) and (0, 2). فتح الحزمة
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5
Use a double integral to find the volume of the solid shown in the figure.
A) 36
B) 24
C) 144
D) 12
E) 48
A) 36
B) 24
C) 144
D) 12
E) 48
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6
Find the volume of the solid bounded above by the surface and below by the plane region R. and R is the region bounded by the graphs of .
A)
B)
C)
D)
E)
and below by the plane region R. and R is the region bounded by the graphs of .
A)
B)
C)
D)
E)
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7
Use a double integral to find the volume of the solid shown in the figure.
__________ cu units.
__________ cu units.
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8
Use a double integral to find the volume of the solid shown in the figure.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Find the volume of the solid bounded above by the surface and below by the plane region R. and R is the region bounded by the graphs of and .
and below by the plane region R. and R is the region bounded by the graphs of and . فتح الحزمة
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10
The population density of a certain city is given by the function
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
E)
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
E)
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11
Use a double integral to find the volume of the solid shown in the figure.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Find the average value of the function over the plane region R. and R is the triangle with vertices , and .
A) 5
B)
C) 25
D)
E)
over the plane region R. and R is the triangle with vertices , and . A) 5
B)
C) 25
D)
E)
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13
Find the volume of the solid bounded above by the surface
And below by the plane region R.
R is the triangle with vertices and .
A)
B)
C)
D)
E)
And below by the plane region R.
R is the triangle with vertices
and .
A)
B)
C)
D)
E)
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14
Use a double integral to find the volume of the solid shown in the figure.
A) 12
B) 96
C) 64
D) 256
E) 384
A) 12
B) 96
C) 64
D) 256
E) 384
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15
Find the volume of the solid bounded above by the surface and below by the plane region R. ; R is the region bounded by .
A)
B)
C)
D)
E)
and below by the plane region R. ; R is the region bounded by .
A)
B)
C)
D)
E)
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16
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
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17
Use a double integral to find the volume of the solid shown in the figure.
__________ cu units.
__________ cu units.
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18
Find the average value of the given function over the plane region R. ; R is the region bounded by the graph of and from to .
A)
B)
C)
D)
E)
over the plane region R. ; R is the region bounded by the graph of and from to .
A)
B)
C)
D)
E)
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19
Use a double integral to find the volume of the solid shown in the figure.
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20
Use a double integral to find the volume of the solid shown in the figure.
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21
Evaluate the double integral
For the given function f(x, y) and the region R.
F(x, y) = 6x + 6y; R is bounded by x = 0, , y = 0 and y = 4.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 6x + 6y; R is bounded by x = 0,
, y = 0 and y = 4.
A)
B)
C)
D)
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22
Find the volume of the solid bounded above by the surface
Z = f(x, y)
And below by the plane region R.
; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).
A)
B)
C)
Z = f(x, y)
And below by the plane region R.
; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).
A)
B)
C)
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23
Evaluate the double integral
For the function and the region R.
and R is the rectangle defined by and .
A) 8
B) 6
C) 2
D) 3
E) 5
For the function
and the region R.
and R is the rectangle defined by and .
A) 8
B) 6
C) 2
D) 3
E) 5
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24
Evaluate the double integral
For the given function f(x, y) and the region R.
F(x, y) = 4x + 2y; R is bounded by x = 0, x = 4, y = 0 and y = x.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 4x + 2y; R is bounded by x = 0, x = 4, y = 0 and y = x.
A)
B)
C)
D)
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25
Evaluate the double integral
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) 0
B) 4
C) -4
D) 1
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) 0
B) 4
C) -4
D) 1
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26
Use a double integral to find the volume of the solid shown in the figure.
A)
B)
C)
D)
A)
B)
C)
D)
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27
Evaluate the double integral
For the given function f(x, y) and the region R.
; R is bounded by and y = x.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
; R is bounded by and y = x.
A)
B)
C)
D)
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28
Find the average value of the given function over the plane region R.
; R is the triangle with vertices (0, 0), (1, 0) and (1, 1).
over the plane region R.
; R is the triangle with vertices (0, 0), (1, 0) and (1, 1). فتح الحزمة
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29
Evaluate the double integral
For the given function f(x, y) and the region R.
F(x, y) = 2y + x; R is the rectangle defined by and .
A)
B)
C)
D) 26
For the given function f(x, y) and the region R.
F(x, y) = 2y + x; R is the rectangle defined by
and .
A)
B)
C)
D) 26
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30
Use a double integral to find the volume of the solid shown in the figure.
A) 6
B) 4
C) 9
D) 14
A) 6
B) 4
C) 9
D) 14
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31
Use a double integral to find the volume of the solid shown in the figure.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Evaluate the double integral
For the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
A) 2.5
B) 3.5e
C) -3.5
D) -2.5
For the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
A) 2.5
B) 3.5e
C) -3.5
D) -2.5
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33
Evaluate the double integral
For the given function f(x, y) and the region R.
F(x, y) = 6x + 12y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
A)
B)
C)
D)
For the given function f(x, y) and the region R.
F(x, y) = 6x + 12y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
A)
B)
C)
D)
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34
Find the average value of the given function over the plane region R.
; R is the region bounded by the graph of and from to .
over the plane region R.
; R is the region bounded by the graph of and from to . فتح الحزمة
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35
Evaluate the double integral
For the given function f(x, y) and the region R.
; R is the rectangle defined by and
A)
B)
C)
D)
For the given function f(x, y) and the region R.
; R is the rectangle defined by and A)
B)
C)
D)
فتح الحزمة
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36
Find the volume of the solid bounded above by the surface
Z = f(x, y)
And below by the plane region R.
; R is the region bounded by , , and .
A)
B)
C)
Z = f(x, y)
And below by the plane region R.
; R is the region bounded by , , and .
A)
B)
C)
فتح الحزمة
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37
Evaluate the double integral
For the function and the region R.
and R is bounded by , , and .
A)
B)
C)
D)
E)
For the function
and the region R.
and R is bounded by , , and .
A)
B)
C)
D)
E)
فتح الحزمة
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38
Evaluate the double integral
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) -10
B) 10e
C) 9
D) -9e
For the given function f(x, y) and the region R.
; R is the rectangle defined by and .
A) -10
B) 10e
C) 9
D) -9e
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39
Use a double integral to find the volume of the solid shown in the figure.
A) 5,996
B) 6,008
C) 6,000
D) 5,994
A) 5,996
B) 6,008
C) 6,000
D) 5,994
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40
Find the average value of the function over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1). فتح الحزمة
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41
Find the volume of the solid bounded above by the surface
And below by the plane region R.
and R is the region bounded by the graphs of and .
A)
B)
C)
D)
E)
And below by the plane region R.
and R is the region bounded by the graphs of and .
A)
B)
C)
D)
E)
فتح الحزمة
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42
Evaluate the double integral for the given function f(x, y) and the region R. Enter your answer as a fraction. ; R is the rectangle defined by and .
for the given function f(x, y) and the region R. Enter your answer as a fraction. ; R is the rectangle defined by and . فتح الحزمة
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43
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
Where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A) per week
B) per week
C) per week
D) per week
E) per week
Where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
A)
per weekB)
per weekC)
per weekD)
per weekE)
per week فتح الحزمة
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44
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where .
A) From the definition follows , so the statement is false.
B) From the definition follows , so the statement is true.
C) From the definition follows , so the statement is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where .
A) From the definition follows
, so the statement is false.B) From the definition follows
, so the statement is true.C) From the definition follows
, so the statement is false. فتح الحزمة
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45
Use a double integral to find the volume of the solid shown in the figure.
فتح الحزمة
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46
Find the average value of the function
Over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
A)
B)
C)
D)
E)
Over the plane region R.
and R is the triangle with vertices (0, 0), (0, 1) and (1, 1).
A)
B)
C)
D)
E)
فتح الحزمة
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47
The Country Workshop's total weekly profit (in dollars) realized in manufacturing and selling its rolltop desks is given by the profit function
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
where x stands for the number of finished units and y stands for the number of unfinished units manufactured and sold each week. Find the average weekly profit if the number of finished units manufactured and sold varies between 180 and 200 and the number of unfinished units varies between 100 and 120 per week. Please round your answer to the nearest dollar, if necessary.
P = $__________ per week.
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48
Evaluate the double integral
for the given function f(x, y) and the region R. Enter your answer as a fraction.
f(x, y) = 0x + 0y; R is bounded by x = 0, , y = 0 and y = 4.
for the given function f(x, y) and the region R. Enter your answer as a fraction.
f(x, y) = 0x + 0y; R is bounded by x = 0,
, y = 0 and y = 4. فتح الحزمة
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49
Evaluate the double integral
for the function and the region R.
and R is the rectangle defined by and .
for the function
and the region R.
and R is the rectangle defined by and . فتح الحزمة
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50
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is the rectangle defined by and .
for the given function f(x, y) and the region R.
; R is the rectangle defined by and . فتح الحزمة
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51
Evaluate the double integral for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 2y + 3x; R is the rectangle defined by and .
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 2y + 3x; R is the rectangle defined by and . فتح الحزمة
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52
Find the average value of the given function
Over the plane region R.
; R is the region bounded by the graph of y = 8x and y = 0 from x = 1 to x = 7.
A)
B)
C)
D)
Over the plane region R.
; R is the region bounded by the graph of y = 8x and y = 0 from x = 1 to x = 7.
A)
B)
C)
D)
فتح الحزمة
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53
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x.
for the given function f(x, y) and the region R.
; R is bounded by x = 0, x = 1, y = 0 and y = x. فتح الحزمة
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54
Evaluate the double integral for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x.
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x. فتح الحزمة
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55
Use a double integral to find the volume of the solid shown in the figure.
فتح الحزمة
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56
The population density of a certain city is given by the function
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
Where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
A)
B)
C)
D)
فتح الحزمة
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57
Evaluate the double integral for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 4x + 8y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1.
for the given function f(x, y) and the region R. Enter your answer as a fraction. f(x, y) = 4x + 8y; R is bounded by x = 1, x = 3, y = 0 and y = x + 1. فتح الحزمة
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58
Find the average value of the given function
F(x, y)
Over the plane region R.
; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
F(x, y)
Over the plane region R.
; R is the triangle with vertices (0, 0), (2, 0) and (2, 2).
A)
B)
C)
D)
فتح الحزمة
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59
Evaluate the double integral
for the function and the region R. Enter your answer as an expression.
and R is bounded by , , and .
for the function
and the region R. Enter your answer as an expression.
and R is bounded by , , and . فتح الحزمة
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60
Evaluate the double integral
for the given function f(x, y) and the region R.
; R is the rectangle defined by and .
for the given function f(x, y) and the region R.
; R is the rectangle defined by and . فتح الحزمة
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61
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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62
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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63
Find the approximate change in z when the point changes from to . ; from to
A)
B)
C)
D)
E)
changes from to . ; from to A)
B)
C)
D)
E)
فتح الحزمة
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64
Find the average value of the given function
f(x, y)
over the plane region R. Enter your answer as a fraction.
; R is the triangle with vertices (0, 0), (5, 0) and (5, 5).
f(x, y)
over the plane region R. Enter your answer as a fraction.
; R is the triangle with vertices (0, 0), (5, 0) and (5, 5). فتح الحزمة
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65
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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66
Find the volume of the solid bounded above by the surface
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the region bounded by , and .
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the region bounded by , and . فتح الحزمة
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67
Find the volume of the solid bounded above by the surface
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the triangle with vertices (0, 0), (4, 0) and (0, 4).
z = f(x, y)
and below by the plane region R. Enter your answer as an expression.
; R is the triangle with vertices (0, 0), (4, 0) and (0, 4). فتح الحزمة
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68
Use a double integral to find the volume of the solid shown in the figure. Enter your answer as an expression.
فتح الحزمة
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69
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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70
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where .
If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then
where . فتح الحزمة
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71
Find the approximate change in z when the point changes from to . ; from to
A)
B)
C)
D)
E)
changes from to . ; from to A)
B)
C)
D)
E)
فتح الحزمة
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72
Find the approximate change in z when the point changes from to . ; from to
A)
B)
C)
D)
E)
changes from to . ; from to A)
B)
C)
D)
E)
فتح الحزمة
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فتح الحزمة
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73
Evaluate the double integral
for the given function f(x, y) and the region R. Enter your answer as an expression.
; R is bounded by and y = x.
for the given function f(x, y) and the region R. Enter your answer as an expression.
; R is bounded by and y = x. فتح الحزمة
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74
Find the average value of the given function
f(x, y)
over the plane region R. Enter your answer as an expression.
; R is the region bounded by the graph of y = 2x and y = 0 from x = 1 to x = 7.
f(x, y)
over the plane region R. Enter your answer as an expression.
; R is the region bounded by the graph of y = 2x and y = 0 from x = 1 to x = 7. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 219 في هذه المجموعة.
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75
Use a double integral to find the volume of the solid shown in the figure. Enter your answer as a formula.
فتح الحزمة
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76
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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77
Find the total differential of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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78
Find the average value of the function
over the plane region R. Enter your answer as an expression.
and R is the triangle with vertices , and .
over the plane region R. Enter your answer as an expression.
and R is the triangle with vertices , and . فتح الحزمة
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79
Find the volume of the solid bounded above by the surface
and below by the plane region R. Enter your answer as a formula.
and R is the region bounded by the graphs of and .
and below by the plane region R. Enter your answer as a formula.
and R is the region bounded by the graphs of and . فتح الحزمة
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80
The population density of a certain city is given by the function
where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
. Enter your answer as an expression.
where the origin (0, 0) gives the location of the government center. Find the population inside the rectangular area described by
. Enter your answer as an expression. فتح الحزمة
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فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 219 في هذه المجموعة.
