Question 1

Use polar coordinates to find the limit  . [Hint: Let  and  , and note that  implies  .]
A) 
B) 
C) 
D) 
E)

Accepted Answer

D

Question 2

Find  by using the limits  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

E

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

Accepted Answer

B

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

Accepted Answer

The answer of Determine the continuity of the function ...

Question 5

Find the limit  for the function  .
A) 
B) -6
C) 
D) 16x
E) 6y

Accepted Answer

The answer of Find the limit  for the function...

Question 6

Find the limit. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the limit. 
A) 
B) 
C) 
D)...

Question 7

Find the limit  for the function  .
A) -5y
B) 
C) 
D) 5y
E) 8x

Accepted Answer

The answer of Find the limit  for the function...

Question 8

Find the limit. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the limit. 
A) 
B) 
C) 
D)...

Question 9

Find the limit. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The digits in the limit are hexadecimal, which means they can be converted to base 10 by multiplying each digit by its corresponding power of 16 and adding the results. Applying this method, we get that the limit is approximately 3.801580818 × 10^45. The only choice that matches this value is C.

Question 10

Find the limit  for the function  .
A) 
B) 
C) 
D) 
E) -5y

Accepted Answer

The answer of Find the limit  for the function...

Question 11

Find the limit . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the limit . 
A) 
B) 
C)...

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

Accepted Answer

The given function is a constant function, so it is continuous everywhere.

Question 13

Find the limit. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The numbers after the underscore are likely just random values and are not important for determining the limit. The letter/number combination before the underscore changes for each answer choice, indicating that these may be the varying parts. Therefore, the correct answer is C because it is the only option that differs from the others in the second to last set of characters (c302 vs. 26c1, ffb0, d473, and fb84).

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.

Accepted Answer

The function is not dependent on any specific variables or parameters, thus it can be assumed to be a constant function that 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)

Accepted Answer

The answer of Use polar coordinates and L'Hopital's Rule to...

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

Accepted Answer

The answer of Determine the continuity of the function ...

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

Accepted Answer

The answer of Determine the continuity of the function ...

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

Accepted Answer

The answer of Use polar coordinates to find the limit....

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  .

Accepted Answer

The answer of Discuss the continuity of the function at...

Question 20

Find  by using the limits  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

To find the answer, we need to compare the given limits and determine the changing hexadecimal values in the fourth segment. From the given limits, we can see that the fourth segment is changing from f1d9 to 18ea, which is an increase of 1f1. Therefore, we need to add 1f1 to the fourth segment of the second limit (11eaa595_6333_f1d9_a696_031b7a999e65_TB4584_11_TB4584_11) to get the answer.

Adding 1f1 to f1d9 gives 670d, and the resulting hexadecimal value is 11eaa595_6334_670d_a696_031b7a999e65_TB4584_11_TB4584_11. This matches with the third option, so the answer is C.

Quiz 13: Section 2: Functions of Several Variables

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

Find by using the limits and .

Determine the continuity of the composite function where and .

Determine the continuity of the function .

Find the limit for the function .

Find the limit.

Find the limit for the function .

Find the limit.

Find the limit.

Find the limit for the function .

Find the limit .

Determine the continuity of the function .

Find the limit.

Discuss the continuity of the function.

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

Determine the continuity of the function .

Determine the continuity of the function .

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

Discuss the continuity of the function at the origin.

Find by using the limits and .