Deck 13: Section 2: Functions of Several Variables

Question 1

Use polar coordinates to find the limit . [Hint: Let and , and note that implies .]

A)
B)
C)
D)
E)

Answer 1

Question 2

Find by using the limits and .

A)
B)
C)
D)
E)

Answer 2

Question 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

Answer 3

continuous for all

Question 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

Question 5

Find the limit for the function .

A)
B) -6
C)
D) 16x
E) 6y

Question 6

Find the limit.

A)
B)
C)
D)
E)

Question 7

Find the limit for the function .

A) -5y
B)
C)
D) 5y
E) 8x

Question 8

Find the limit.

A)
B)
C)
D)
E)

Question 9

Find the limit.

A)
B)
C)
D)
E)

Question 10

Find the limit for the function .

A)
B)
C)
D)
E) -5y

Question 11

Find the limit .

A)
B)
C)
D)
E)

Question 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

Question 13

Find the limit.

A)
B)
C)
D)
E)

Question 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.

Question 15

Use polar coordinates and L'Hopital's Rule to find the limit.

A)
B)
C)
D)
E)

Question 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

Question 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

Question 18

Use polar coordinates to find the limit. [Hint: Let and , and note that implies .]

A)
B)
C)
D)
E) limit does not exist

Question 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 .

Question 20

Find by using the limits and .

A)
B)
C)
D)
E)

Question 21

Use spherical coordinates to find the limit [Hint: Let and , and note that implies .]

A) 6
B) 9
C) 1
D) 7
E)

Question 22

Find the limit for the function .

A)
B)
C)
D)
E)