Deck 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Question 1

Use the graph shown to determine if the limit exists. If it does, find its value.

A) 1
B) 3
C) 0
D) does not exist

Answer 1

B

Question 2

Use the TABLE feature of a graphing utility to find the limit.

A) 2
B) 0
C) 1
D) does not exist

Answer 2

B

Question 3

Use the grid to graph the function. Find the limit, if it exists

A) 1
B) -2
C) -8
D) does not exist

Answer 3

C

Question 4

Find the limit algebraically.

A) -6
B) 1
C) 0
D) 6

Question 5

Use the graph shown to determine if the limit exists. If it does, find its value.

A) 4
B) 3
C) 5
D) does not exist

Question 6

Use the grid to graph the function. Find the limit, if it exists

A) -2
B) -6
C) -8
D) does not exist

Question 7

Use the TABLE feature of a graphing utility to find the limit.

A) 2
B) -2
C) 0
D) does not exist

Question 8

Use the TABLE feature of a graphing utility to find the limit.

A) -1
B) 0
C) 1
D) does not exist

Question 9

Use the grid to graph the function. Find the limit, if it exists

A) 0
B) 1
C) 5
D) does not exist

Question 10

Use the grid to graph the function. Find the limit, if it exists

A) -1
B) 3
C) -2
D) does not exist

Question 11

Use the grid to graph the function. Find the limit, if it exists

A) 12
B) 11
C) 2
D) does not exist

Question 12

Use the graph shown to determine if the limit exists. If it does, find its value.

A) 1
B) -1
C) 4
D) does not exist

Question 13

Find the limit algebraically.

A) -18
B) 9
C) 3
D) does not exist

Question 14

Use the TABLE feature of a graphing utility to find the limit.

Question 15

Use the TABLE feature of a graphing utility to find the limit.

A) 27
B) 9
C) 0
D) does not exist

Question 16

Use a graphing utility to find the indicated limit rounded to two decimal places.

A) 2.04
B) 2.96
C) 3.00
D) 2.00

Question 17

Use the TABLE feature of a graphing utility to find the limit.

A) 0
B) -18
C) 18
D) does not exist

Question 18

Use the grid to graph the function. Find the limit, if it exists

A) -5
B) 1
C) 5
D) does not exist

Question 19

Use the graph shown to determine if the limit exists. If it does, find its value.

A) 0
B) 1
C) 2
D) does not exist

Question 20

Find the limit algebraically.

A) 0
B) 6
C) -6
D) 1

Question 21

Find the limit algebraically.

A) 100
B) -352
C) 256
D) 144

Question 22

Find the limit algebraically.

A) -125
B) -5
C) 125
D) 25

Question 23

Find the limit algebraically.

A) 15
B) 0
C) 29
D) does not exist

Question 24

Find the limit algebraically.

A) -5
B) 0
C) 5
D) does not exist

Question 25

Find the limit algebraically.

A)
B) 0
C) 8
D) does not exist

Question 26

Find the limit algebraically.

A) - 59
B) - 75
C) - 12
D) does not exist

Question 27

Find the limit algebraically.

A) Does not exist
B) 3
C) 1
D) 6

Question 28

Find the limit algebraically.

A) -3
B) -1
C) 3
D) 1

Question 29

Find the limit algebraically.

A) 2
B) 0
C) 4
D) Does not exist

Question 30

Find the limit algebraically.

A) Does not exist
B) 5
C) 0
D) -8

Question 31

Find the limit algebraically.

A) -2
B) 2
C) 0
D) does not exist

Question 32

Find the limit algebraically.

A) 31
B) -1
C) 1
D) 33

Question 33

Find the limit algebraically.

A) -5
B) 0
C) 5
D) does not exist

Question 34

Find the limit algebraically.

A) 0
B) -1
C) 5
D) Does not exist

Question 35

Find the limit algebraically.

A) -8
B) -1,000
C) -10
D) 8,000

Question 36

Find the limit algebraically.

A) -1
B) 1
C) 2
D) does not exist

Question 37

Find the limit algebraically.

A) -4
B) 4
C) Does not exist
D) 0

Question 38

Find the limit algebraically.

A) 0
B) 6
C) Does not exist
D) -6

Question 39

Find the limit algebraically.

A) -48
B) -237
C) 249
D) -21

Question 40

Find the limit algebraically.

A) Does not exist
B) -2
C) 1
D) -4

Question 41

Find the limit algebraically.

A) -16
B) 0
C) 16
D) does not exist

Question 42

Use the graph of y = g(x) to answer the question.
Does xist? If it does, what is it?

A) yes; 0
B) yes; 3
C) yes; 4
D) does not exist

Question 43

Use the graph of y = g(x) to answer the question.
Find f(1).

A) 3
B) 4
C) 0
D) -1

Question 44

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = 3;

A) 108
B) 57
C) 30
D) 90

Question 45

Use the graph of y = g(x) to answer the question.
What is the domain of g?

Question 46

Use the graph of y = g(x) to answer the question.
Find the y-intercept(s), if any, of g.

A) 3
B) 0
C) -1
D)

Question 47

Use the graph of y = g(x) to answer the question.
Find f(-1).

A) 1
B) 0
C) 4
D) -1

Question 48

Use the graph of y = g(x) to answer the question.
Find f(2)

A) 1
B) 2
C)
D) 3

Question 49

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = -3;

A) 18
B) -9
C) -12
D) Does not exist

Question 50

Find the limit algebraically.

Question 51

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = 3; f(x) = 5x + 3

A) -5
B) 3
C) 5
D) -3

Question 52

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = 4;

Question 53

Use the graph of y = g(x) to answer the question.
Find f(-4).

A) -4
B) 0
C) 2
D) 1

Question 54

Use the graph of y = g(x) to answer the question.

A) 1
B) 0
C) 4
D) does not exist

Question 55

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = 9;

A) 3
B) Does not exist
C) 13
D)

Question 56

Find the limit algebraically.

A) 4
B) 0
C) -4
D) does not exist

Question 57

Find the limit algebraically.

Question 58

Find the limit as x approaches c of the average rate of change of the function from c to x.
c = -4;

A) 0
B) 16
C) 48
D) 32

Question 59

Use the graph of y = g(x) to answer the question.
What is the range of g?

Question 60

Find the one-sided limit.

A) 0
B) -1
C) 4
D) does not exist

Question 61

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 62

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 63

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 64

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 65

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 66

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 67

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 68

Find the one-sided limit.

Question 69

Find the one-sided limit.

A) 3
B) -6
C) 6
D) -3

Question 70

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 71

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 72

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 73

Find the one-sided limit.

A) 8
B) 0
C) 4
D) does not exist

Question 74

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 75

Determine whether f is continuous at c.

A) continuous
B) not continuous

Question 76

Find the one-sided limit.

A) -2
B) 2
C) 0
D) does not exist

Question 77

Determine whether f is continuous at c.

Question 78

Find the one-sided limit.

A) Does not exist
B) 5
C) -8
D) 0

Question 79

Determine whether f is continuous at c.

A) not continuous
B) continuous

Question 80

Find the one-sided limit.

A) 13
B) -5
C) 1
D) 7