تكلم مع الذكاء الاصطناعي
Deck 13: Section 2: Functions of Several Variables
ملء الشاشة (f)
سؤال
Use polar coordinates to find the limit ![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634f_6867_a696_339935b1d4b9_TB4584_11_TB4584_11.jpg)
. [Hint: Let ![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634f_b688_a696_79f8c2547c5d_TB4584_11_TB4584_11.jpg)
and ![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634f_dd99_a696_b9724a3c3590_TB4584_11_TB4584_11.jpg)
, and note that ![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634f_dd9a_a696_fb93ac8f6044_TB4584_11_TB4584_11.jpg)
implies ![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_04ab_a696_9539c65e91bb_TB4584_11_TB4584_11.jpg)
.]
A)![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_2bbc_a696_67ca53947071_TB4584_11_TB4584_11.jpg)
B)![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_2bbd_a696_6d9c4bcd85f1_TB4584_11_TB4584_11.jpg)
C)![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_52ce_a696_a3812ea4a91b_TB4584_11_TB4584_11.jpg)
D)![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_79df_a696_abbd85f121c2_TB4584_11_TB4584_11.jpg)
E)![<strong>Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6350_a0f0_a696_33c47bd5f574_TB4584_11_TB4584_11.jpg)
. [Hint: Let and , and note that implies .]A)
B)
C)
D)
E)
سؤال
Find 
by using the limits 
and 
.
A)
B)
C)
D)
E)
by using the limits and .A)
B)
C)
D)
E)
سؤال
Determine the continuity of the composite function 
where 
and 
.
A) continuous except at
B) continuous for all
C) continuous for all
D) continuous except at
E) continuous everywhere
where and .A) continuous except at
B) continuous for all
C) continuous for all
D) continuous except at
E) continuous everywhere
سؤال
Determine the continuity of the function 
.
A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
سؤال
Find the limit 
for the function 
.
A)
B) -6
C)
D) 16x
E) 6y
for the function .A)
B) -6
C)
D) 16x
E) 6y
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the limit 
for the function 
.
A) -5y
B)
C)
D) 5y
E) 8x
for the function .A) -5y
B)
C)
D) 5y
E) 8x
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the limit 
for the function 
.
A)
B)
C)
D)
E) -5y
for the function .A)
B)
C)
D)
E) -5y
سؤال
Find the limit . 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the continuity of the function 
.
A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
سؤال
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Discuss the continuity of the function. 
A)
is continuous everywhere except at those points 
such that 
.
B)
is continuous everywhere except at those points 
such that 
.
C)
is continuous at those points 
such that 
.
D)
is continuous only when 
.
E)
is continuous everywhere in the xy-plane.
A)
is continuous everywhere except at those points such that .B)
is continuous everywhere except at those points such that .C)
is continuous at those points such that .D)
is continuous only when .E)
is continuous everywhere in the xy-plane. سؤال
Use polar coordinates and L'Hopital's Rule to find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the continuity of the function 
.
A) continuous except at
B) continuous for
C) continuous except at
D) continuous except at
E) continuous for
.A) continuous except at
B) continuous for
C) continuous except at
D) continuous except at
E) continuous for
سؤال
Determine the continuity of the function 
.
A) continuous except at
B) continuous except at
C) continuous for all
D) continuous for all
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous for all
D) continuous for all
E) continuous everywhere
سؤال
Use polar coordinates to find the limit. [Hint: Let ![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_1e6e_a696_350d410e42c7_TB4584_11_TB4584_11.jpg)
and ![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_1e6f_a696_a956aeda859a_TB4584_11_TB4584_11.jpg)
, and note that ![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_4580_a696_95385fc9b554_TB4584_11_TB4584_11.jpg)
implies ![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_4581_a696_27ef5ef690f3_TB4584_11_TB4584_11.jpg)
.] ![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_6c92_a696_7d381cd023e1_TB4584_11_TB4584_11.jpg)
A)![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_bab3_a696_6fe5669bc8fd_TB4584_11_TB4584_11.jpg)
B)![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634d_e1c4_a696_b94079cf628e_TB4584_11_TB4584_11.jpg)
C)![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634e_08d5_a696_9346477f317f_TB4584_11_TB4584_11.jpg)
D)![<strong>Use polar coordinates to find the limit. [Hint: Let and , and note that implies .] </strong> A) B) C) D) E) limit does not exist <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_634e_2fe6_a696_95fce9df5130_TB4584_11_TB4584_11.jpg)
E) limit does not exist
and , and note that implies .] A)
B)
C)
D)
E) limit does not exist
سؤال
Discuss the continuity of the function at the origin. 
A) f is discontinuous at (0,0).
The discontinuity can be removed by setting
instead of 9.
B) f is discontinuous at
.
The discontinuity can be removed by setting
instead of 9.
C) f is discontinuous at
.
The discontinuity can be removed by setting
= 0 instead of 9.
D) f is discontinuous at
.
The discontinuity cannot be removed by changing the value of f at
.
E) f is continuous at
.
A) f is discontinuous at (0,0).
The discontinuity can be removed by setting
instead of 9.B) f is discontinuous at
.The discontinuity can be removed by setting
instead of 9.C) f is discontinuous at
.The discontinuity can be removed by setting
= 0 instead of 9.D) f is discontinuous at
.The discontinuity cannot be removed by changing the value of f at
.E) f is continuous at
. سؤال
Find 
by using the limits 
and 
.
A)
B)
C)
D)
E)
by using the limits and .A)
B)
C)
D)
E)
سؤال
Use spherical coordinates to find the limit ![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635b_ebc6_a696_1170883c48d2_TB4584_11_TB4584_11.jpg)
[Hint: Let ![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635c_12d7_a696_f1d0b68eeca4_TB4584_11_TB4584_11.jpg)
and ![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635c_8808_a696_9122a0a35798_TB4584_11_TB4584_11.jpg)
, and note that ![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635c_af19_a696_5746d17ecc2c_TB4584_11_TB4584_11.jpg)
implies ![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635c_d62a_a696_3d32750ef9bd_TB4584_11_TB4584_11.jpg)
.]
A) 6
B) 9
C) 1
D) 7
E)![<strong>Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]</strong> A) 6 B) 9 C) 1 D) 7 E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_635c_fd3b_a696_2dada95d9732_TB4584_11_TB4584_11.jpg)
[Hint: Let and , and note that implies .]A) 6
B) 9
C) 1
D) 7
E)
سؤال
Find the limit 
for the function 
.
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
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العب
ملء الشاشة (f)
Deck 13: Section 2: Functions of Several Variables
1
Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]
A)
B)
C)
D)
E)
. [Hint: Let and , and note that implies .]A)
B)
C)
D)
E)
2
Find by using the limits and .
A)
B)
C)
D)
E)
by using the limits and .A)
B)
C)
D)
E)
3
Determine the continuity of the composite function where and .
A) continuous except at
B) continuous for all
C) continuous for all
D) continuous except at
E) continuous everywhere
where and .A) continuous except at
B) continuous for all
C) continuous for all
D) continuous except at
E) continuous everywhere
continuous for all
4
Determine the continuity of the function .
A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
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5
Find the limit for the function .
A)
B) -6
C)
D) 16x
E) 6y
for the function .A)
B) -6
C)
D) 16x
E) 6y
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6
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Find the limit for the function .
A) -5y
B)
C)
D) 5y
E) 8x
for the function .A) -5y
B)
C)
D) 5y
E) 8x
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8
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Find the limit for the function .
A)
B)
C)
D)
E) -5y
for the function .A)
B)
C)
D)
E) -5y
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11
Find the limit .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Determine the continuity of the function .
A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous except at
D) continuous except at
E) continuous everywhere
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13
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Discuss the continuity of the function.
A) is continuous everywhere except at those points such that .
B) is continuous everywhere except at those points such that .
C) is continuous at those points such that .
D) is continuous only when .
E) is continuous everywhere in the xy-plane.
A)
is continuous everywhere except at those points such that .B)
is continuous everywhere except at those points such that .C)
is continuous at those points such that .D)
is continuous only when .E)
is continuous everywhere in the xy-plane. فتح الحزمة
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15
Use polar coordinates and L'Hopital's Rule to find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Determine the continuity of the function .
A) continuous except at
B) continuous for
C) continuous except at
D) continuous except at
E) continuous for
.A) continuous except at
B) continuous for
C) continuous except at
D) continuous except at
E) continuous for
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17
Determine the continuity of the function .
A) continuous except at
B) continuous except at
C) continuous for all
D) continuous for all
E) continuous everywhere
.A) continuous except at
B) continuous except at
C) continuous for all
D) continuous for all
E) continuous everywhere
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18
Use polar coordinates to find the limit. [Hint: Let and , and note that implies .]
A)
B)
C)
D)
E) limit does not exist
and , and note that implies .] A)
B)
C)
D)
E) limit does not exist
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19
Discuss the continuity of the function at the origin.
A) f is discontinuous at (0,0).
The discontinuity can be removed by setting instead of 9.
B) f is discontinuous at .
The discontinuity can be removed by setting instead of 9.
C) f is discontinuous at .
The discontinuity can be removed by setting = 0 instead of 9.
D) f is discontinuous at .
The discontinuity cannot be removed by changing the value of f at .
E) f is continuous at .
A) f is discontinuous at (0,0).
The discontinuity can be removed by setting
instead of 9.B) f is discontinuous at
.The discontinuity can be removed by setting
instead of 9.C) f is discontinuous at
.The discontinuity can be removed by setting
= 0 instead of 9.D) f is discontinuous at
.The discontinuity cannot be removed by changing the value of f at
.E) f is continuous at
. فتح الحزمة
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20
Find by using the limits and .
A)
B)
C)
D)
E)
by using the limits and .A)
B)
C)
D)
E)
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21
Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]
A) 6
B) 9
C) 1
D) 7
E)
[Hint: Let and , and note that implies .]A) 6
B) 9
C) 1
D) 7
E)
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22
Find the limit for the function .
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
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