Mathematics 15 Sec EN 1 Quiz

 Mathematics 15 Sec EN 1 Quiz | chatbot las positas  community college

Question 1

Determine whether the given function is continuous. If it is not, identify where it is discontinuous.  

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         continuous everywhere

 

Question 2

Use analytic methods to find the limit as   for the given function.  

·         920  

·         240  

·         –920  

·         –240

  

Question 3

For the given function, find the average rate of change over the specified interval.

  over     

·         0  

·         –2  

·         6  

·         –34  

·         34

 

Question 4

A certain calling card costs 6.8 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 68 cent connection fee. If   is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent.

 

  

·         $0  

·         $0.68  

·         $0.75  

·         $0.82

  

Question 5

This problem contains a function and its graph, where  . Use the graph to determine, as well as you can,  . Check your conclusion by using the function to determine   analytically. 

·         4  

·         1  

·         3  

·         0 

 

Question 6

Use properties of limits and algebraic methods to find the limit, if it exists.  

 

Question 7

This problem contains a function and its graph, where  . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically.

 

Question 8

Determine whether the given function is continuous. If it is not, identify where it is discontinuous.  

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         continuous everywhere

 

Question 9

Use the graph of   and the given c-value to find  .  

·         –8 

·         -6

·         3  

·         –4

  

Question 10

 

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by  . Describe any discontinuities for C(p). Explain what each discontinuity means.  

·         C(p) is discontinuous at  . This means that not all pollution can be removed.  

·         C(p) is discontinuous at  . This means that none of the pollution can be removed.  

·         C(p) is continuous everywhere.  

·         C(p) is discontinuous at  . This means that not all pollution can be removed.  

·         C(p) is discontinuous at  . This means that none of the pollution can be removed.

 

Question 11

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.  

·         limit = 3, vertical asymptote  

·         limit = 6, horizontal asymptote  

·         limit = 6, vertical asymptote  

·         limit = 3, horizontal asymptote  

 

Question 12

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by  , where t is the number of days on the job. What is the domain for this application?

 

Question 13

Use the graph of   and the given c-value to find  .  

·         2  

·         –2  

·         6  

·         0

 

Question 14

Use the graph of   and the given c-value to find  .  

·         –6  

·         0  

·         2  

·         6

  

Question 15

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. 

·         limit = 0, vertical asymptote  

·         limit = 0, horizontal asymptote  

·         limit = 2, horizontal asymptote  

·         limit = 2, vertical asymptote 

 

Question 16

Use properties of limits and algebraic methods to find the limit, if it exists.  

 

Question 17

Use properties of limits and algebraic methods to find   if the limit exists.

·         0  

·         10 

·         ∞  

·         –10  

·         5

 

Question 18

Complete the table and use it to predict the limit, if it exists.

 

x              f(x)

0.9         

0.99       

0.999    

↓           ↓

1              ?

↑           ↑

1.001    

1.01       

1.1            

–5  

5  

–4  

4

 

Question 19

Use the graph of   and the given c-value to find  .

 

 

 

 

  

·         –6  

·         –5  

·         –1  

·         3

  

Question 20

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold.    

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         discontinuous at     

·         continuous everywhere

 

Question 21

A graph of   is shown and a c-value is given. For this problem, use the graph to find  .  

·         10  

·         –15  

·         0  

·         15

 

Question 22

Graph the function using a window with   and  . What does the graph indicate about     

·         –5  

·         5  

·         30  

·         0

Question 23

Use properties of limits and algebraic methods to find the limit, if it exists.  

·         –45  

·         54  

·         45  

·         –54

 

Question 24

Use analytic methods to find the limit as   for the given function.  

·         –1500  

·         1500  

·         –620  

·         620

  

Question 25

 

Determine whether the given function   is continuous. If   is not continuous, identify where it is discontinuous and which condition(s) fails to hold.  

·         is discontinuous at   since   is not defined and   does not exist.  

·         is discontinuous at   since   is not defined and   does not exist.  

·         is discontinuous at   since   is not defined and   does not exist.  

·         is continuous.  

·         is discontinuous at   since   is not defined and   does not exist.

 

Question 26

A graph of   is shown and a c-value is given. For this problem, use the graph to find  . 

·         0    

·         2  

·         –6 

·         –4

 

Question 27

This problem contains a function and its graph, where  . Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically.

 

Question 28

Use the graph of   and the given c-value to find  . 

·         –6

·         0 

·         8  

·         2

 

Question 29

Use properties of limits and algebraic methods to find the limit, if it exists.  

·         97 

·         99 

·         94 

·         102

 

Question 30

Use properties of limits and algebraic methods to find the limit, if it exists. 

 

Question 31

Use the graph of   and the given c-value to find  .  

·         –8 

·         3 

·         –1

 

 Question 32

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function.

Is C continuous at  ?  

·         Yes  

·         No

 

Question 33

Determine whether the function is continuous or discontinuous at the given x-value.  

·         continuous 

·         discontinuous

Question 34

If   and  , find  .  

·         20  

·         6 

·         –2 

·         –14

  

Question 35

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by  , where t is the number of days on the job. Is this function continuous for all values of t?  

·         Yes  

·         No

 

Question 36

Use the graph of   and the given c-value to find  . 

·         4  

·         0  

·         2  

·         –6

 

Question 37

Complete the table and use it to predict the limit, if it exists.

 

   

 

 x             f(x)

–0.51    

–0.501    

–0.5001                 

↓           ↓

–0.5       ?

↑           ↑

–0.4999                 

–0.499    

–0.49      

 

  

44.0

  

–22.0

  

22.0

  

–0.5

  

 

Question 38

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by  , where t is the number of days on the job. Is this function continuous at  

·         Yes  

·         No

 

 

Question 39

A graph of   is shown and a c-value is given. For this problem, use the graph to find  .  

·         0  

·         5  

·         –5

·         –6

Question 40

Use analytic methods to find any point of discontinuity for the given function.

 

Question 41

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.

·         limit = 10, horizontal asymptote

·         limit = 10, vertical asymptote

·         limit = 4, horizontal asymptote

·         limit = 4, vertical asymptote  

 

Question 42

Determine whether the function is continuous or discontinuous at the given x-value.  

·         continuous  

·         discontinuous

 

Question 43

For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value.  

·         discontinuous  

·         continuous

 

Question 44

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by  , where t is the number of days on the job. Is this function continuous for all     

·         Yes  

·         No

 

Question 45

A graph of   is shown and a c-value is given. For this problem, use the graph to find  .  

·         0

·         –15

·         15

  

 

Question 46

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.  

·         18 

·         4  

·         0

 

Question 47

This problem contains a function and its graph, where  . Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine   analytically. 

·         3  

·         0  

·         4  

·         1

 

Question 48

Use the graph of   and the given c-value to find  .  

·         –6  

·         –6  

·         –1  

·         3