Deck 3: Introduction to the Derivative

Question 1

Estimate the limit numerically.

A)
B)
C)
D)
E)

Answer 1

Question 2

Use the graph to compute .

Answer 2

8

Question 3

Compute .

A)
B)
C)
D)
E)

Answer 3

Question 4

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 5

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 6

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 7

Use the graph to compute

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

Question 8

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 9

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 11

The number of visitors, in millions of visitors per year, to Hawaii in the years 1985 to 1993 can be approximated by where t = 0 represents June 30,1985. During the same period, visitor spending can be approximated by where t = 0 represents June 30,1985.Assuming the trends in the models above continue indefinitely, numerically estimate . Please round the answers to the nearest hundredth.

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

Question 12

Use the graph to compute

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

Question 13

Use the graph to compute the given quantity.

A)
B)
C)
D)
E)

Question 14

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 15

Estimate the limit numerically.

A)-2
B)
C)
D)
E)

Question 16

Estimate the limit numerically.

A)
B)
C)
D)1
E)

Question 17

Use the graph to compute the following quantities. Please enter your answer as two numbers, separated by a comma.

Question 18

Use the graph to compute

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

Question 19

Estimate the limit numerically.

A)
B)
C)
D)
E)

Question 20

If is the Dow Jones Average at time and , is it possible that the Dow will fluctuate indefinitely into the future?

A)yes
B)no

Question 21

The graph of a function is given. Determine whether is continuous on its domain.

A)Continuous
B)Discontinuous

Question 22

Determine what, if any, value to assign to f ( a )to make f continuous at x = a . ;

A)
B)
C)
D)
E)No value of f (0)will make it continuous at .

Question 23

Determine what, if any, value to assign to f ( a )to make f continuous at x = a . ;

A)
B)
C)
D)
E)No value of will make it continuous at .

Question 24

Use a graph of f or some other method to determine what, if any, value to assign to f ( a )to make f continuous at x = a .

A)
B)
C)
D)
E)No value of will make it continuous at .

Question 25

The graph of a function is given. Determine whether is continuous on its domain.

A)Continuous
B)Discontinuous

Question 26

Use a graph to determine whether the function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

A)The points of discontinuity: -2, 0.
B)The point of discontinuity: 0.
C)The function is continuous on its domain.
D)The point of discontinuity: 2.
E)The points of discontinuity: 2, 0.

Question 27

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

A)The point of discontinuity: .
B)The points of discontinuity: .
C)The function is continuous on its domain.
D)The point of discontinuity: .
E)The points of discontinuity: -2, 0.

Question 28

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

A)The points of discontinuity: .
B)The point of discontinuity: .
C)The points of discontinuity: .
D)The point of discontinuity: .
E)The function is continuous on its domain.

Question 29

Determine what, if any, value to assign to f ( a )to make f continuous at x = a . ;

Question 30

The graph of a function is given. Determine whether is continuous on its domain.

A)Discontinuous
B)Continuous

Question 31

Determine what, if any, value to assign to f ( a )to make f continuous at x = a . ;

A)
B)
C)
D)
E)No value of f (0)will make it continuous at 0.

Question 32

Use a graph to determine whether the function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

Question 33

The graph of a function is given. Determine whether is continuous on its domain.

A)Continuous
B)Discontinuous

Question 34

The graph of a function is given. Determine whether is continuous on its domain.

A)Discontinuous
B)Continuous

Question 35

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

A)The function is continuous on its domain.
B)The point of discontinuity: .
C)The point of discontinuity: .
D)The points of discontinuity: .
E)The points of discontinuity: .

Question 36

Determine what, if any, value to assign to f ( a )to make f continuous at x = a . ;

Question 37

Draw the graph of a function that is continuous on its domain but not continuous at any integer.

A)
B)
C)
D)
E)

Question 38

Compute the derivative function algebraically.

Question 39

The graph of a function is given. Determine whether is continuous on its domain.

A)Discontinuous
B)Continuous

Question 40

Use a graph to determine whether the function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.

Question 41

Calculate the limit algebraically.

A)37
B)36
C)-36
D)108
E)144

Question 42

Calculate the limit algebraically.

A)11
B)1.2
C)-5
D)2.2
E)6

Question 43

Calculate the limit algebraically.

A)-0.25
B)2
C)0.3
D)-4.0
E)None of these

Question 44

Calculate the limit algebraically.

A)
B)
C)
D)
E)

Question 45

Calculate the limit algebraically.

A)-17
B)-8.5
C)8
D)4
E)3

Question 46

Calculate the limit algebraically.

A)-2.75
B)-0.75
C)-3
D)2.75
E)12

Question 47

Calculate the limit algebraically.

A)9
B)-9
C)5
D)4
E)2.25

Question 48

Give an example of a function that is not continuous at but is not discontinuous there either.

Question 49

Calculate the limit algebraically.

Question 50

Calculate the limit algebraically.

A)
B)
C)0
D)
E)

Question 51

Calculate the limit algebraically.

A)
B)
C)
D)
E)

Question 52

Calculate the limit algebraically.

A)1
B)2
C)-1
D)0.5
E)-2

Question 53

Calculate the limit algebraically.

A)6
B)-2
C)0
D)8
E)10

Question 54

Calculate the limit algebraically.

A)25
B)50
C)5
D)-5
E)30

Question 55

Does this limit exist? Select the correct answer.

A)does not exist
B)exists

Question 56

Calculate the limit algebraically.

A)
B)
C)
D)
E)

Question 57

Find all points of discontinuity of the function.

A)
B)
C) , ,
D) ,
E)The function is continuous everywhere.

Question 58

Calculate the limit algebraically.

A)
B)
C)
D)
E)

Question 59

Find all points of discontinuity of the function.

A) , ,
B)
C) ,
D)
E)The function is continuous everywhere.

Question 60

The cost of fighting crime in the U.S. increased steadily in the period 1982-1999. Total spending on police, courts, and prisons can be approximated, respectively, by billion dollars billion dollars billion dollars where t is time in years since 1980. Compute to two decimal places.

A)0.27
B)0.52
C)0.42
D)0.37
E)0.32

Question 61

Calculate the limit algebraically.

Question 62

Calculate the average rate of change of the given function (Inflation (%)of Budget deficit (% of GNP))over the interval .

A)5
B)1
C)8
D)-0.5
E)-20

Question 63

Calculate the average rate of change of the given function over the interval .

A)-10
B)-4
C)1.5
D)5
E)-5

Question 64

Calculate the average rate of change of the given function over the intervals , where h = 1, 0.1, 0.01, 0.001, and 0.0001. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.) Complete the table.

A)dq -6.4 -64 -640 -6,400 -64,000
B)dq 8.1 65.61 641.601 6,401.6001 64,001.60001
C)dq 1.7 1.61 1.601 1.6001 0
D)dq 1.7 1.61 1.601 1.6001 55,998.40001
E)dq 1.7 1.61 1.601 1.6001 1.60001

Question 65

Calculate the average rate of change of the given function over the intervals , where h = 1, 0.1, 0.01, 0.001, and 0.0001. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.) Complete the table.

A)dq -0.3000 -0.3529 0.0000 0.0000 -0.3600
B)dq 1.5000 17.6471 179.6407 1,799.6401 17,999.6400
C)dq -0.3000 -0.3529 -0.3593 -0.3599 0.0000
D)dq -1.8000 -18.0000 -180.0000 -1,800.0000 -18,000.0000
E)dq -0.3000 -0.3529 -0.3593 -0.3599 -0.3600

Question 66

Calculate the average rate of change of the given function over the interval .

A)1.9
B)5.4
C)1.4
D)-10.8
E)5.3

Question 67

Calculate the average rate of change of the given function over the interval .

A)19
B)15
C)9
D)11
E)7

Question 68

Calculate the average rate of change of the given function over the interval . x 3 4 5 6 f ( x )5 15 4 9

Question 69

Calculate the average rate of change of the given function f over the intervals , where h = 5, 0.5, 0.05, 0.005, and 0.0005. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.) Complete the table.

A)dq 145.6 569.5 -644 -6,404 496,071.0025
B)dq 96 73.5 -9 71.025 71.0025
C)dq -49.6 -496 -4,960 -49,600 -496,000
D)dq 96 73.5 71.25 71.025 71.0025
E)dq 96 297 71.25 71.025 71.0025

Question 70

Calculate the average rate of change of the given function over the interval .

A)838.5
B)139.75
C)41.93
D)253.5
E)76.05

Question 71

Calculate the average rate of change of the given function f over the intervals , where h = 5, 0.5, 0.05, 0.005, and 0.0005. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.) Complete the table.

A)dq 13 8.5 8.05 8.005 8.0005
B)dq 40 4 0.4 0.000025 0.0005
C)dq 40 4 0.4 0.04 0.00000025
D)dq 200 2 0.02 0.0002 0.000002
E)dq 40 4 0.4 0.04 0.004

Question 72

Calculate the limit algebraically.

Question 73

Calculate the average rate of change of the given function over the interval .

A)800
B)4,000
C)-50
D)-800
E)-200

Question 74

Calculate the average rate of change of the given function over the interval .

A)
B)
C)
D)
E)

Question 75

The chart shows the total annual support for the arts in the U.S. by federal, state, and local government in 1995-2003 as a function of time in years ( represents 1995)together with the regression line. Over the period the average rate of change of government funding for the arts was _____ the rate predicted by the regression line.

A)equal to
B)greater than
C)less than

Question 76

Calculate the average rate of change of the given function over the interval .

A)-$50,000
B)-$0
C)-$100,000
D)$50,000
E)$50

Question 77

Calculate the average rate of change of the given function over the interval .

A)30.25
B)121
C)14
D)-121
E)56

Question 78

Calculate the average rate of change of the given function over the interval .

A)-44
B)40
C)-4
D)4
E)-40

Question 79

Calculate the average rate of change of the given function over the interval .

Question 80

Calculate the average rate of change of the given function over the interval .

A)360
B)6
C)-36
D)-60
E)-6