Question 1

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 2

A study of driving costs of 1992 model subcompact (four-cylinder) cars found that the average cost (car payments, gas, insurance, upkeep, and depreciation), measured in cents/mile, is approximated by the function ​  ​
Where x denotes the number of miles (in thousands) the car is driven in a year. What happens to the average cost as the number of miles driven increases without bound?
​
A) It approaches 2,640 ¢/mi.
B) It approaches 19 ¢/mi.
C) It increases without bound.
D) It becomes infinitely small.

Accepted Answer

The answer of A study of driving costs of 1992...

Question 3

Find the indicated limit.
​

Accepted Answer

The answer of Find the indicated limit.
​ ...

Question 4

Use the graph of the given function f to determine  at the indicated value of  , if it exists. ​  ​
A) 
B) 
C) 
D) The limit does not exist

Accepted Answer

The answer of Use the graph of the given function...

Question 5

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 6

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 7

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 8

Select the correct graph of the function f and evaluate  if it exists. ​  ​
A) ​  ​ 
B) ​  ​ The limit does not exist
C) ​  ​ 
D) ​  ​

Accepted Answer

The answer of Select the correct graph of the function...

Question 9

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 10

Use the graph of the given function  to determine  at the indicated value of  .
​  ​  __________

Accepted Answer

The answer of Use the graph of the given function...

Question 11

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 12

Find  given that  and  .

Accepted Answer

The answer of Find  given that  and ...

Question 13

A study of driving costs of 1992 model subcompact (four-cylinder) cars found that the average cost (car payments, gas, insurance, upkeep, and depreciation), measured in cents/mile, is approximated by the function
​  ​
where x denotes the number of miles (in thousands) the car is driven in a year. What happens to the average cost as the number of miles driven increases without bound? Express your answer to the nearest tenth, if necessary.
​
It approaches __________ ¢/mi.

Accepted Answer

The answer of A study of driving costs of 1992...

Question 14

Find the indicated limit, if it exists. Otherwise, answer no solution.
​

Accepted Answer

The answer of Find the indicated limit, if it exists....

Question 15

Complete the table by computing  at the given values of  . Use these results to estimate at  if it exists.   4.9 4.99
4)999
5)001
5)01
5)1       ​​
A) ​  4.9 4.99 4.999 5.001 5.01 5.1  0.025 0.000025 0.000003 0.000003 0.0025 0.025 ​ ​  ​
B) ​​  4.9​ 4.99 4.999 ​5.001 5.01 5.1  400 40,000 4,000,000 4,000,000 40,000 400  ​
C) ​​  4.9 4.99 4.999 5.001 5.01 5.1  0.0025 0.000025 0 0 0.000025 0.0025 ​ ​  ​
D) ​  4.9 4.99 4.999 5.001 5.01 5.1  400 40,000 4,000,000 4,000,000 40,000 400 ​The limit does not exist.​

Accepted Answer

The answer of Complete the table by computing  at...

Question 16

Find the indicated limit.
​  ​

Accepted Answer

The answer of Find the indicated limit.
​  ​...

Question 17

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 18

Complete the table by computing  at the given values of  . Use these results to estimate at  if it exists.   6.9 6.99
6)999
7)001
7)01
7)1       ​​
A) ​  6.9 6.99 6.999 7.001 7.01 7.1  53.91 55.7901 55.979001 56.007001 56.0701 56.71 ​ ​  ​
B) ​​  6.9​ 6.99 6.999 ​7.001 7.01 7.1  54.61 55.8601 55.986001 56.014001 56.1401 57.41  ​
C) ​​  6.9 6.99 6.999 7.001 7.01 7.1  54.41 55.8401 55.984001 56.012001 56.1201 57.21 ​ ​  ​
D) ​  6.9 6.99 6.999 7.001 7.01 7.1  55.01 55.9001 55.990001 56.018001 56.1801 57.81 ​The limit does not exist.​

Accepted Answer

The answer of Complete the table by computing  at...

Question 19

Use the graph of the function f to determine  and  . ​  ​  ​
A) ​  and 
B) ​  and 
C)  and 
D)  and

Accepted Answer

The x-intercept occurs when the graph intersects the x-axis, so it is where y = 0. Looking at the graph, we can see that the x-intercepts occur at approximately x = -4 and x = 2.5.
The y-intercept occurs when the graph intersects the y-axis, so it is where x = 0. Looking at the graph, we can see that the y-intercept occurs at approximately y = 2.
Choice B matches these values closely.

Question 20

Find the limit, if it exists. ​  ​
A) 
B) 
C) 
D) The limit does not exist

Accepted Answer

As the given expression contains no variables or parameters, it represents a constant value. Therefore, the limit does not depend on any sequence of inputs and is simply the value of the constant, which cannot be determined from the given information.

Quiz 2: Functions, Limits, and the Derivative

Find the limit.

Find the indicated limit.

Use the graph of the given function f to determine at the indicated value of , if it exists.

Find the limit.

Find the limit.

Find the limit.

Select the correct graph of the function f and evaluate if it exists.

Find the limit.

Use the graph of the given function to determine at the indicated value of . __________

Find the limit.

Find given that and .

Find the indicated limit, if it exists. Otherwise, answer no solution.

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 4.9 4.99 4) 999 5) 001 5) 01 5) 1

Find the indicated limit.

Find the limit.

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 6.9 6.99 6) 999 7) 001 7) 01 7) 1

Use the graph of the function f to determine and .

Find the limit, if it exists.

Quiz 2: Functions, Limits, and the Derivative

Find the limit. ​

Find the indicated limit. ​

Use the graph of the given function f to determine at the indicated value of , if it exists. ​ ​

Find the limit. ​

Find the limit. ​

Find the limit. ​

Select the correct graph of the function f and evaluate if it exists. ​ ​

Find the limit. ​

Use the graph of the given function to determine at the indicated value of . ​ ​ __________

Find the limit. ​

Find given that and .

Find the indicated limit, if it exists. Otherwise, answer no solution. ​

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 4.9 4.99 4) 999 5) 001 5) 01 5) 1 ​​

Find the indicated limit. ​ ​

Find the limit. ​

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 6.9 6.99 6) 999 7) 001 7) 01 7) 1 ​​

Use the graph of the function f to determine and . ​ ​ ​

Find the limit, if it exists. ​ ​

Find the limit.

Find the indicated limit.

Use the graph of the given function f to determine at the indicated value of , if it exists.

Find the limit.

Find the limit.

Find the limit.

Select the correct graph of the function f and evaluate if it exists.

Find the limit.

Use the graph of the given function to determine at the indicated value of . __________

Find the limit.

Find the indicated limit, if it exists. Otherwise, answer no solution.

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 4.9 4.99 4) 999 5) 001 5) 01 5) 1

Find the indicated limit.

Find the limit.

Complete the table by computing at the given values of . Use these results to estimate at if it exists. 6.9 6.99 6) 999 7) 001 7) 01 7) 1

Use the graph of the function f to determine and .

Find the limit, if it exists.